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COFxREGHT DEPOSIT. 



ESSENTIALS 

OF 

FORMAL LOGIC 



BY 



MICHAEL J. MAHONY, S.J. 

Professor of Logic and Metaphysics, 

St. John's College, 

Fordham University, New York 




THE ENCYCLOPEDIA PRESS, INC. 

New York 

1918 









Permissu superiorum 



Nihil obstat 

Arthur J. Scanlan, D.D. 
Censor 

Imprimatur 

John Cardinal Farley 

Archbishop of New York 



Copyright, 1918 

THE ENCYCLOPEDIA PRESS, INC. 

New York 

MAR 19 1918 
©CI.A494149 



PREFACE 

This little book has been compiled for beginners who 
intend to complete a full course of philosophy in two 
years. In such a course Formal Logic is supposed to 
be finished by the end of the first three months. This 
requirement demands not a treatise, but a text-book on 
Formal Logic, which will comprise the essentials of the 
subject and serve as a basis for further development 
and illustration in the hands of an experienced teacher. 

Conciseness is one of the chief aims of the book. 
This characteristic respects the individuality and free- 
dom of the teacher, while for the sake of the student, 
thoroughness, it is to be hoped, is not sacrificed. 
Hence controverted points and sometimes examples 
which the judicious teacher no doubt will suggest are 
omitted. 

The author gratefully acknowledges his indebtedness 
to the admirable Latin works of J. S. Hickey, O. Cist., 
and C. Frick, S.J. Some of the examples illustrative 
of the forms of reasoning have been taken or adapted 
from the more exhaustive treatise in English of G. H. 
Joyce, S.J. 

Fordham University, 
Feast of St. Michael, 29th Sept., 1917. 



CONTENTS 

Preliminary Notions 

PHILOSOPHY— Definition— Divisions— Educational and 
Cultural Value — Ethical Value — Relation between 
Philosophy and the Christian Religion 1 

LOGIC — Natural and Acquired — Definition — Material and 
Formal Objects — Correctness and Truth of Thought — 
Divisions 6 

MINOR LOGIC or DIALECTICS— Definition— Divisions. 9 

Part I 

THE FIRST ACT OF THE MIND— SIMPLE 
APPREHENSION 

Chapter I 

SIMPLE APPREHENSION AND ALLIED NOTIONS 
— Definition of Simple Apprehension — Subjective, Ob- 
jective and Representative Character — Other Names 
for — Matjerial and Formal Objects — Comprehension 
and Extension — Mental Processes involved in Simple 
Apprehension 11 

Chapter II 

CLASSIFICATION OF SIMPLE APPREHENSIONS- 
IDEAS — A. According to their Origin — B. According 
to the Objects which they represent — Direct and 
reflex universal Ideas — Predicables and Predicaments 
— C. According to the Perfection with which they 
represent their Objects 19 

Chapter III 

THE OUTWARD EXPRESSION OF IDEAS— Signs- 
Definition — Division — Words — Categorematic — 
Syncategorematic — Terms — Division — Supposition 
of terms 30 



Part II 
THE SECOND ACT OF THE MIND — JUDGMENT 

Chapter I 

THE NATURE OF JUDGMENT — Definition — Pre- 
requisites— Matter and Form — Division of Judgment — 
Proposition — Subect, Predicate, Copula — Nature of the 
Copula — What it expresses — Division of Propositions 
— Quantity and Quality of Propositions 35 

Chapter II 

LAWS THAT REGULATE THE DISTRIBUTION OF 
SUBJECT AND PREDICATE— Applied to A, E, 
I, O Propositions — Simple, Complex and Compound 
Propositions — Reduction of Compound Propositions 
to their Logical Forms 43 

Chapter III 

MODAL PROPOSITIONS— Definition— Division ... 47 

Chapter IV 

RELATIVE PROPERTIES OF PROPOSITIONS— 
Opposite Propositions — Definition — Species of Oppo- 
sition—Square Opposition— Laws of Opposition . . 48 

Chapter V 

AEQUIPOLLENCE OR EQUIVALENCE — Definition 
— Examples — Rule. 49 

Chapter VI 

CONVERSION OF PROPOSITIONS— Definition— Dif- 
ferent Kinds— j Rules 50 

Part III 
THE THIRD ACT OF THE MIND — REASONING 

Chapter I 

NATURE OF THE ACT OF REASONING — Pre- 
requisites — Matter and Form of Definition — Basic 
Principles of 51 



Chapter II 

EXPRESSION OF THE ACT OF REASONING— Syllo- 
gism — Definition — Technical Terms involved in . . 54 

Chapter III 

RULES OF THE SYLLOGISM— Enumeration— Proof 
of each 57 

Chapter IV 

MOODS AND FIGURES— Definition— Number of pos- 
sible Premises — Invalid Premises — Valid Premises. 
Figures — Definition — Forms of — Special Rules of 
each — Moods that are valid in each — Mnemonic 
Lines 61 

Chapter V 

REDUCTION— Definition— Meaning of Letters in the 
Mnemonic Words — Direct and Indirect Reduction 64 

Chapter VI 

HYPOTHETICAL SYLLOGISM— Definition— Laws of— 
Rules of Different Kinds of — Fallacies incident to — 
Purely Hypothetical Syllogism 67 

Chapter VII 

THE DISJUNCTIVE SYLLOGISM — Definition — Two 
Moods of — Rules — Fallacies of 69 

Chapter VIII 

ABRIDGED AND CONJOINED SYLLOGISMS— Def- 
inition of abridged Syllogism — The Enthymeme — 
Forms of — Fallacies of — Examples — Conjoined Syl- 
logism — Epicheireme — Sorites — Dilemma — Rules of . 71 

Chapter IX 

INDUCTION— Analytic and Synthetic Judgments— Prob- 
lem of Induction — Definition of Induction — Steps in 
the Process, Observation, Hypothesis, Verification, 



Generalization, Basic Principles of Induction — Caus- 
ality — Uniformity of Nature — Two Kinds of Induction 
— Ultimate Justification of Induction 75 

METHODS OF INDUCTION— Agreement— Difference 
— Residues — Concomitant Variations 81 

Chapter X 

ARGUMENT FROM ANALOGY— Definition and Nature 
— Analogy of Proportion — of Resemblance — Argu- 
ment from Example 83 

Chapter XI 
FALLACIES— Different Forms of 85 

Chapter XII 

DEFINITION— Nature of— ^Nominal and Real— Genetic 
— Descriptive — Essential — Rules of Definition ... 87 

Chapter XIII 

DIVISION— Definition— Different Kinds of Parts— Real 
and Logical Unit — Rules of Division 89 

Part IV 
METHOD 

Chapter I 
DEFINITION— Synthetic and Analytic 92 

Chapter II 
RULES OF METHOD— Rules for Study 94 

FINIS 



FORMAL LOGIC 

Preliminary Notions 

1. PHILOSOPHY. The word "philosophy" means 
the love or study of wisdom. By "wisdom" the 
ancients meant the knowledge of all things human and 
divine which make for right living, as well as the 
causes by which these things are related or hang 
together. Hence the aim of philosophy is to answer, 
in as far as reason is capable of doing so, the last zvhy 
of all things that are. Philosophy is therefore usually 
defined : The science of all things from the point of 
view of their highest or last causes, in so far as this 
knowledge can be attained by the light of natural 
reason. 

2. EXPLANATION OF THE DEFINITION— 
"Science" is a knowledge of a thing through its 
cause. A cause in its widest sense is that by which 
a thing is, becomes, or is known. Philosophy, then, 
is a science because, like all other sciences, it furnishes 
us with a systematized body of truths which, resting 
ultimately on self-evident principles, are united to one 
another like the links of a chain by an orderly process 
of demonstration. 

"of all things" — Each of the other natural sciences 
treats of some special department of things, as chem- 
istry, astronomy, medicine, etc., while philosophy takes 
in a larger field of vision. It embraces the sum total 
of all things in one complete view. 

"highest or last causes" — This characteristic of 
philosophical knowledge which aims at answering the 
last "why" of all reality differentiates philosophy from 
1 



2 ESSENTIALS OF FORMAL LOGIC 

all other natural sciences. Other natural sciences fur- 
nish the more immediate or proximate, but not the 
ultimate causes of the objects of their study. Hence 
philosophy helps to satisfy the yearning of the human 
mind to explore, as far as it is given to reason to do 
so, the utmost limits of knowledge. 

"by the light of natural reason" — In this way is 
philosophy marked off from sacred or dogmatic 
theology. The latter takes its facts and truths from 
divine revelation. Philosophy depends upon the natural 
human faculties to acquire its data and to deduce con- 
clusions from them. 

3. THE DIVISIONS OF PHILOSOPHY. It is 
divided into: 

Logic, which lays down the rules of right reason- 
ing and treats of the means given us by the Author of 
nature to acquire the knowledge of truth. 

Metaphysics, again divided into General and 
Special. The former, called also Ontology, treats of 
the properties of Being in general. The latter applies 
the notions and principles of Ontology to the primary 
classes of Substance and investigates their natures and 
properties. It comprises : 

Cosmology, which treats of the nature and origin 
of the visible world, of the laws to which it is subject 
and of the nature and constituent elements of bodies 
in general ; 

Psychology, which treats of living beings, but prin- 
cipally of the human soul ; 

Natural Theology, which treats of God in as far 
as reason enables us to fathom His Divine nature. 

Moral Philosophy, which discusses the principles 
of morality and the duties we owe to God and to our 
fellow men, considered both as individuals and as 
members of society. 



FORMAL LOGIC 3 

4. EDUCATIONAL AND CULTURAL VALUE 
OF PHILOSOPHY. 

Man has an inborn longing to know the ultimate 
reasons of things. This longing philosophy in a 
measure satisfies. 

The mental effort which the study of philosophy 
calls forth imparts, as perhaps no other study does, 
strength and keenness to the intellectual powers. 

It furnishes the mind with a reasoned conviction 
of the fundamental principles upon which rests all 
scientific knowledge. It sets forth on reasoned grounds 
the essential duties of man to his Creator, of the state 
to its citizens and of the citizens to the state, of man 
to his fellowmen and to himself. 

By the light of sound philosophical principles the 
divinely authorized teaching of supernatural faith 
may be more clearly set forth and defended; vital 
problems of state and private conduct are analyzed 
and solved ; false theories of philosophers and scientists 
are criticised and refuted; it unifies the conclusions 
of the particular sciences; it helps to form soundness 
of judgment ; it develops men of thought. 

5. ETHICAL VALUE OF PHILOSOPHY. It is 
the nature of thought to find its way into action. "The 
will of man is by his reason swayed" (Shakespeare). 
Leo XIII says: "It has been implanted in man by 
nature to follow reason as the guide of his actions, and 
therefore, if the understanding go wrong in anything, 
the will easily follows. Hence it comes about that 
wicked opinions, whose seat is in the understanding, 
flow into human actions and make them bad. On the 
other hand, if the mind of man be healthy and strongly 
grounded in solid and true principles, he will assuredly 
be a source of great blessings, both as regards the 
good of individuals and as regards the common weal." 



4 ESSENTIALS OF FORMAL LOGIC 

6. THE RELATION BETWEEN PHILOSOPHY 
AND THE CHRISTIAN RELIGION. 

a. Viewed from different stand-points, philosophy is 
both independent of, and dependent upon, Theology. 
It is independent : (a) by reason of its object, namely, 
"the ultimate causes of all things in as far as they can 
be known by the light of natural reason", (b) By 
reason of the source from which philosophical knowl- 
edge springs — the light of natural reason. 

b. Philosophy is dependent upon Theology (a) in as 
far as the light of reason, which belongs to the natural 
order, ought to be subservient to the light of Revela- 
tion, which belongs to the supernatural order. Just 
as the scientifically demonstrated conclusions of chem- 
istry must be reasonably accepted in physics, or as 
the acknowledged decisions of our Supreme Court 
are accepted, in legal matters, by other Courts, so 
should the acknowledged truths of Revelation be ac- 
cepted by natural science, (b) The guidance of reason 
which is liable to error, and therefore inferior, ought 
to submit to the guidance and correction of revealed 
truth which is absolutely infallible and therefore 
superior. 

"Through the revelation made by the Son of God, 
a fulness of truth was brought within reach of the 
human mind of which men had previously no notion. 
And if it be true, as the ancients had it, that truth is 
the food of the mind, on which it lives and thrives, 
the revelation through the Redeemer formed an inex- 
haustible store from which the human mind might 
evermore draw new increase of the knowledge which 
is its life. . . . 

"The human mind could adopt either of two atti- 
tudes towards revelation. It might accept revelation 
as truth communicated by God, and make this truth 



FORMAL LOGIC 5 

the criterion and guiding principle of its speculations. 
If it did this, revelation became an end to which 
natural knowledge was to be subservient. . . . 

"Again, the human mind, in virtue of its natural 
freedom of election, might abandon the objective 
standpoint and fall back upon its own subjective 
resources. It might permit its own reason to deal 
with revelation in a more unseemly fashion ; it might 
give reason the first place and revelation the second, 
so that instead of reason being subject to revelation, 
revelation should be accommodated to the subjective 
opinions of the individual ; or, on occasion, entirely 
denied. This, no doubt, would be a perversion of 
right order, but just as man can set himself against the 
divinely-established order in the sphere of morals, so 
can he set himself in opposition to the divine order in 
the sphere of knowledge". (Stockl — Hist. Phil., Part 
II, § 55). 



LOGIC 

Preliminary NotionB 

7. LOGIC is either natural or acquired. The first 
is that inborn or natural disposition to use one's facul- 
ties rightly in the attainment of truth. The second is 
that same natural disposition cultivated by training. 
The latter is the subject of the present treatise. It is 
a necessary study. For untrained reason is liable to 
err, especially in the solution of more difficult problems. 

It may be here noted that any attempt to philosophize 
at all must presuppose that the human mind can attain 
truth. The trustworthiness therefore of the human 
faculties of knowledge must be taken for granted. 

That is, they can, by their own nature, attain truth. 
Otherwise philosophy would be impossible. 

8. DEFINITION OF LOGIC. The word \6yo, 
signifies both "thought" and the expression of thought 
or language — word. Thought again necessarily repre- 
sents some object — we cannot think without thinking of 
something. Logic, then, treats of all three — thought, 
language and objects. But since in the very nature 
of things thought comes before language, it follows 
that Logic treats primarily and directly of thought, 
and secondarily and indirectly of language and objects. 

Since Logic then has primarily to do with thought 
or the operations of the rational or intellectual powers 
of the soul, it is usually defined as : 

That art and science which directs the operations 
of reason in the attainment of truth. 

9. EXPLANATION OF THE DEFINITION— 
"Art" — An art is a right method or way of doing 

6 



PRELIMINARY NOTIONS 7 

something. The thing which logic sets out to do is to 
point the way to think aright. And the right way to 
attain this end is indicated by a system of definite 
rules. In so far, then, as logic sets forth a collection 
of rules to direct the mind aright in the way to truth, 
it is an art. We may distinguish, however, the im- 
parting of the mere knowledge of these rules from 
the actual use of them. The former is called Logica 
docens, the latter, Logica uteris. Logic is an art in 
both senses. 

"science" — Science, as we have seen, is the knowl- 
edge of things through their causes. In as far as 
logic, then, gives the reasons or causes why the rules 
it lays down for right thinking are valid, it is a science. 

"which directs" — Sometimes men violate the rules 
of right thinking and reason ill. Hence to prevent 
this, certain rules of direction must be known and 
applied. 

"operations of reason" — These operations are ideas, 
judgments, and reasoning. They form the sub- 
ject matter (material object) of logic. These same 
mental operations may be the subject matter (material 
object) of different sciences. But in that case the 
stand-point from which these operations are viewed 
(formal object) will in each case be different for the 
different sciences. Psychology, for instance, con- 
siders these operations from the point of view of their 
nature and origin ; rhetoric with a view of using 
them for the purpose of persuasion, while it is the 
province of Logic to direct them as means of attaining 
truth. To direct, then, the operations of reason 
towards the attainment of truth, is the formal object 
of Logic. Hence we say that the same material object 
may be viewed under different formalities. 

To ensure that these operations will issue in truth, 



8 ESSENTIALS OF FORMAL LOGIC 

two distinct aspects of their truth-giving value must 
be considered — firstly their conformity to the rules or 
laws that govern their right procedure as merely 
subjective acts. This secures their correctness. By 
correctness is meant freedom from contradiction and 
inconsistency. Secondly their conformity to objective 
reality. It is in this sense they are said to be true. 
Hence it may happen that these operations of reason, 
or as they are often called intellectual operations, may 
be correct in their procedure without being true in their 
content, and true in their content without being cor- 
rect in their procedure. From this distinction follows 
the two- fold 

10. DIVISION OF LOGIC— MINOR LOGIC 
(called also Dialectics and Formal Logic), which has 
to do directly and primarily with the correctness of 
our thought-operations and secondarily and indirectly 
with the latter aspect, namely the truth of our mental 
operations ; 

MAJOR LOGIC (also called Critical and Material 
Logic), which has to do primarily and directly with 
the latter aspect, the truth, namely, of these same 
operations, and indirectly and secondarily with their 
correctness. 

Many modern authors use the name "Formal 
Logic" instead of the usual Scholastic term "Minor 
Logic" and the Aristotelian term "Dialectics". The 
philosophy of Kant has popularized the term 
"Formal Logic". But the Kantian concept of 
this part of Logic is essentially different from 
the meaning which Scholasticism has assigned to 
it. In the philosophy of Kant the necessary 
grooves or laws which the mind must follow in 
its operations of reason have their origin solely 
in the mind ; they are of the mind and in the mind. 



DIALECTICS 9 

We must think, Kant would say, according to 
these necessary laws because our minds, ante- 
cedently to all experiences of reality, are con- 
stituted that way. 

Scholasticism, on the other hand, accounts for 
these laws of thought, not because our minds are 
originally furnished by nature with these neces- 
sary laws or "forms", but because we discover 
through experience that reality which is inde- 
pendent of the mind is constituted according to 
those laws, and that, too, antecedently to our 
knowing them. 

Kant conceives the laws of thought as "forms" 
native to the mind and therefore as having no 
objective value. Hence he calls the science of 
these "forms" "Formal Logic". Scholasticism 
admits these laws are in the mind but not of the 
mind. They are rather engendered in the mind 
by objective reality. They put us therefore in 
touch with reality. Hence "Formal Logic" does 
not mean to Scholasticism what it means to 
Kantianism. 

MINOR LOGIC OR DIALECTICS 

11. DEFINITION — Dialectics ( SiaKiymreai ) treats 
of the processes of reasoning or discursive thought. It 
may be defined as : A collection of rules scientifically 
demonstrated by which the intellect is directed to think 
correctly. Hence the subject matter or material object 
of dialectics is the "operations of the intellect or 
reason" ; its formal object is "to direct these operations 
in the way of correct thinking". 

12. DIVISION — Since man is by nature charac- 
terized by the power of reasoning, and since reasoning 



10 ESSENTIALS OF FORMAL LOGIC 

involves judgments and judgments involve ideas, dia- 
lectics will treat in turn of each of these mental 
operations. Again each of these mental processes has 
its outward expression in language, namely term, 
proposition, and syllogism. Hence dialectics will treat 
of "terms", "propositions" and "syllogisms" as the 
outward signs or expressions respectively of "ideas", 
"judgments" and "reasoning". 

Besides in the pursuit and attainment of truth the 
human mind, as we shall see later on, naturally pro- 
ceeds along certain lines, ways or roads. These path- 
ways in the acquisition of truth are explained by what 
is called Method (fieri. 666t). 

To sum up then, Minor Logic or Dialectics will 
treat of : 

I. SIMPLE APPREHENSION OR IDEA AND 

TERM 

II. JUDGMENT AND PROPOSITION 

III. REASONING AND THE SYLLOGISM 

IV. METHOD 



Part I 

THE FIRST ACT OF THE MIND- 
SIMPLE APPREHENSION 



Chapter I 
Simple Apprehension and Allied Notions 

13. DEFINITION— Nominal— Simple apprehension 
(apprehendere) is the act of laying hold of, or grasp- 
ing something. 

Real — The act by which the mind lays hold of an 
object mentally without affirming or denying anything 
about it. 

EXPLANATION— "The act by which the mind" 
— Simple apprehension, then, is an act of the mind. 
As such it must necessarily be something within the 
mind as in its subject. Hence simple apprehension, as 
an act of the mind, is said to be something subjective. 

"lays hold on an object". Since it is impossible 
for the mind "to lay hold or grasp" without laying 
hold of or grasping something, that something is called 
the OBJECT of simple apprehension. Hence every 
simple apprehension must necessarily be objective as 
well as subjective. When the mind "lays hold of" or 
apprehends an object, it is said to know, to perceive, 
to become aware of an object. 

The object perceived may, of course, have no real 
existence in nature. It may be only a possible object, 
as when I apprehend "a golden mountain". Or again, 
11 



12 ESSENTIALS OF FORMAL LOGIC 

the manner or mode of the object's existence in nature 
may be quite different from the mode of its existence 
as perceived by the mind. For instance I may have a 
simple apprehension of the object "honesty". I per- 
ceive "honesty" in and by itself as if it had a manner 
or mode of existence in nature by itself, yet "honesty" 
does not exist in nature independently and by itself, 
but as the quality inherent in some object. 

Lastly the object perceived must be represented in 
some way in the mind ; otherwise we could not discern 
one object from another. Hence every simple appre- 
hension must needs be representative, that is, its object 
must in some way be reproduced in the mind. How 
this reproduction or representation of the object takes 
place in the mind is not discussed at present. We only 
assert the fact. Summing up then we arrive at the 
conclusion that every "simple apprehension" must of 
necessity be : 

A. SUBJECTIVE 

B. OBJECTIVE 

C. REPRESENTATIVE 
"mentally". By this word of the definition we 

guard against confounding simple apprehension as an 
act of the intellect with sensitive perception or a sensi- 
tive picture in the imagination, which is by philosophers 
called a phantasm. Imagining is altogether different 
from conceiving. Sense perception and phantasms 
men have in common with brutes, while simple appre- 
hension, as an act of the intellect, is the prerogative 
of man. 

The object of sense-perception is always concrete, 
individual, bound up with matter. It is limited by 
time, place; it is here and now and this, as this par- 
ticular triangle (drawn upon the blackboard with 
yellow chalk). The object of a simple apprehension 



SIMPLE APPREHENSION AND ALLIED NOTIONS 13 

on the contrary is conceived in the mind as abstracted 
from all limitations of matter — of nowness, hereness, 
thisness, size, color, as a triangle conceived as "a plane 
figure bounded by three straight lines". It is an object 
common to many individuals, that is, it is universal. 
The universal is not picturable. 

This distinction is fundamental in all sound systems 
of philosophy. Failure to recognize this distinction 
has issued both in the past and present in Idealism on 
the one hand and Sensism on the other. 

"without affirming or denying, etc.". "Apprehen- 
sion" for this reason is called "simple", and is 
distinguished from judgment. A judgment always 
says something is or is not something else. Hence an 
act of judgment always involves two objects of 
thought, a simple apprehension only one. 

Understand well, then, that the simple apprehension 
is simple not because the object apprehended may not 
be complex, as "the last-rose-of-summer", but precisely 
because in its character of simple apprehension we do 
not affirm or deny anything about it, that is, we do 
not form a judgment about it. 

14. OTHER NAMES FOR SIMPLE APPRE- 
HENSION. Simple Apprehension is also spoken of 
as an idea, concept, notion, mental word, mental term. 
Each of these words but emphasizes some particular 
aspect of the same thing. Thus while simple appre- 
hension expresses more emphatically the subjective 
and objective aspect of the first mental act, idea (like- 
ness, picture) lays stress upon its representative value ; 
concept (conceptus) directs attention to the spiritual 
generation of the object in the mind. Again, since to 
apprehend is to know (noscere), to take notice of an 
object, hence the result of apprehension is called a 
notion (notus). Simple apprehension is called a 



14 ESSENTIALS OF FORMAL LOGIC 

mental word, because by it the object is expressed in 
the mind, and a mental term because the simple appre- 
hension may be viewed as a mental form or likeness 
of the object, which de-term-ines the mind to know 
this object rather than that. 

It is customary, as it is more convenient in Logic, 
to speak of ideas rather than of simple apprehensions. 

15. THE OBJECT OF AN IDEA. That which 
the idea represents to the mind is called the object of 
the idea. Objects manifest themselves to us; that is 
we know them by certain marks. These marks are 
called "attributes", "qualities", "forms", "determina- 
tions", "notes". For instance the paper I write upon 
is "white", "rectangular", "thin", "made of linen", 
"smooth". These are called its "notes", etc. We may 
come to know a greater or less number of these 
"notes". 

THE MATERIAL OBJECT OF AN IDEA— The 
object itself, viewed as the subject of all its notes, 
whether we advert to them or not, is called the material 
object of the idea. 

THE FORMAL OBJECT OF AN IDEA. That 
same object, viewed as manifesting to the mind certain 
notes which we here and now actually come to know, 
is the Formal Object of the idea. The Formal and 
Material Object are not two really independent objects, 
but the same object viewed from different points of 
view. 

16. THE COMPREHENSION AND EXTEN- 
SION OF AN IDEA. By the comprehension of an 
idea is meant the collection of notes which the idea 
implies ; by the extension of an idea is meant the num- 
ber of individual objects to which the idea applies. 
It follows then as a general rule that as the compre- 
hension of an idea is increased, its extension is 



SIMPLE APPREHENSION AND ALLIED NOTIONS 15 

decreased, and vice versa, in any series of ideas that 
have an orderly relation one to the other. 

English writers use the term connotation for com- 
prehension and denotation for extension. 

17. OTHER MENTAL PROCESSES IN- 
VOLVED IN SIMPLE APPREHENSION. That 
we may the better understand what follows, it is 
necessary to explain certain mental processes which 
ideas or simple apprehensions involve. They are : 

ATTENTION, an act by which the mind directs 
its powers of thought to one object out of many which 
lie in its field of vision. To apprehend an object the 
mind must needs attend to it. Hence every simple 
apprehension involves an act of attention, whether 
voluntary or involuntary. 

ABSTRACTION, which is a species of attention. 
It is an act by which the mind withdraws its attention 
from all other "notes" which naturally co-exist in an 
object, and fastens it upon one alone. By abstraction the 
mind does not deny the other notes ; it simply prescinds 
from them. For instance we may consider the "color" 
of a flower to the neglect of the "odor", or we may 
fasten our attention upon the characteristics of the 
nature of man — "rational" and "animal" apart from 
the individualizing notes of this particular man. Since 
the object of a simple apprehension is universal, the 
mind in conceiving it abstracts from individualizing 
qualities of that object. Hence an act of simple ap- 
prehension involves also an act of ABSTRACTION. 

The object in which the "notes" or attributes are 
found is called the subject, and the note or attribute in 
itself is called a form, quality, attribute, etc. (Cf. 15). 

REFLECTION, an act by which the mind contem- 
plates its own acts or states. Reflection is two-fold: 

Psychological Rejection, when the mind regards its 



16 ESSENTIALS OF FORMAL LOGIC 

own acts, or states as facts or modifications of one's 
own soul; 

Ontological Reflection, when the mind regards its 
own acts or states not precisely as its own, but as 
representative of objects. 

How reflection enters into an act of simple appre- 
hension will appear in the explanation of INTEN- 
TION. 

INTENTION may be considered subjectively as an 
act of the mind, or objectively as an OBJECT upon 
which the mind's eye is riveted. But when logicians 
use the word "intention" they usually understand it 
in an objective sense. It is in this latter sense we 
shall consider it at present. 

Intention is two-fold — first or direct intention and 
second or reflex intention. It may be observed that 
a clear knowledge of these terms is essential to the 
understanding of the Scholastic system of philosophy. 

These terms express what experience tells us are 
the two stages through which the mind passes in the 
formation of universal ideas. An accurate under- 
standing of their meaning may be difficult for begin- 
ners. Yet the light which their study will throw on 
subsequent logical processes will repay our efforts. 

A FIRST or DIRECT INTENTION is an object 
of our first thought or of our first views of things. 
I become aware by my sense of sight, for instance, 
of a "triangle". It will be right-angled, or equi- 
lateral, or scalene, or isosceles ; it will be drawn 
with chalk of a certain color; it will be of a certain 
area; it will be here, now and this. It will have all 
the individuating "notes" of a material particular 
"triangle". At the same instant my intellect spon- 
taneously abstracts from this triangle perceived by 
sense all its individuating peculiarities — its thisness, 



SIMPLE APPREHENSION AND ALLIED NOTIONS 17 

nowness, hereness, its color, size, etc., leaving before 
my first direct intellectual gaze only what constitutes 
a "triangle", namely "a plane figure bounded by three 
straight lines". This object of thought then, "plane 
figure, etc.", upon which the mind directly and at first 
hand rivets its attention, is called a "first or direct 
intention". 

A SECOND or REFLEX INTENTION has for 
its object something altogether different from that of 
the "first intention". The object of the "first or direct 
intention" is some reality as it is in itself set out before 
and independent of the mind. The object of the 
second or reflex intention is the CONCEPT in the 
mind of the object of the "first intention". The "first 
intention" looks out directly upon its object — "the 
plane figure bounded by three straight lines". The 
second intention looks back into the mind for its 
object, the concept namely of "the plane figure, etc.". 
The second intention therefore is a concept of a con- 
cept. Its object is a concept in the mind. 

The concept or idea which the mind forms of the 
object of the "first or direct intention" — the plane 
figure bounded by three straight lines — is called a 
"direct universal". It neither includes the individuat- 
ing notes nor does it explicitly exclude them. It simply 
neglects them. Considered abstractedly, it is in itself 
not yet known to be either singular or universal. Yet 
the notes it represents really exist independently of 
the mind. 

The concept which the mind forms of the concept 
of the object of the "first intention" is called a reflex 
universal, because the formation of such a concept 
called for a reflex act of the mind. This reflex uni- 
versal positively excludes all the individualizing notes. 
Because the mind perceives the Concept within the 



18 ESSENTIALS OF FORMAL LOGIC 

mind itself in the manner in which it is therein — and 
the concept is in the mind in a state of abstraction 
as a result of its first intention. Hence it expresses 
a certain number of "notes" that are capable of being 
pluralized in many. The object of thought in the case 
of the reflex universal embraces both the object I 
conceive (the direct universal) and the way I conceive 
it. Hence the reflex universal is a logical or con- 
ceptual entity in the mind, but with a foundation in 
reality. 

Examples of second intentions are "animal" as a 
genus, "man" as a species, "rational" as a specific 
difference. 

It is called SECOND Intention because it neces- 
sarily presupposes a First Intention. It likewise pre- 
supposes acts of reflection. 

ANALYSIS means the act of separating- or taking 
the elements of a thing apart. Analysis of an idea 
is the act of resolving an idea into its constituent 
parts whether in its comprehension or extension. The 
formation of a simple apprehension which results in 
a universal idea always involves analysis, because the 
mind by its power of abstraction eliminates individual 
or accidental characters. 

SYNTHESIS is the act of putting things together. 
Synthesis of ideas means that operation by which the 
mind unites two or more ideas into one. Thus a 
composite idea is formed by the union of simple 
ideas, as when the concept of "man" is formed by 
uniting the concepts "animal" and "rational". 

COMPARISON is the act by which the mind 
directs its attention now to one idea, now to another, 
in order to detect the relations between them, — such 
relations, for instance, as agreement, difference, 
similarity. 



Chapter II 
Classification of Ideas 

Ideas are classified according to the different stand- 
points from which you view them. These classifications 
will help to give your knowledge an orderly arrange- 
ment as well as afford an insight into the workings of 
your own mind. Strive to see these different classes 
of ideas with the eyes of your mind as clearly as you 
see bodies with your bodily eyes. This classification 
we owe to the philosophical studies of centuries. Ideas 
then may be divided 

18. According to their ORIGIN into FACTITIOUS 
and PRIMITIVE ideas. 

A PRIMITIVE idea is one which is formed in 
the mind by the very presence of its object. If the 
object is extra-mental the idea of it is said to be 
direct, if the object is intra-mental the idea of it is 
said to be reflex. Primitive ideas are sometimes called 
intuitive. 

FACTITIOUS ideas are those which the mind 
forms by grouping together two or more primitive 
ideas, or by the analysis o-f a primitive idea into its 
elements. 

These factitious ideas are either arbitrary or dis- 
cursive. Arbitrary ideas are those that are formed 
at will or at the bidding of fancy by the union of two 
or more primitive ideas, as a "golden mountain", or 
by the analysis of a primitive idea into its elements. 

Discursive ideas are those that are the outcome of 
a reasoning process, as the "idea of God". 

Some ideas may be partly primitive and partly fac- 
19 



20 ESSENTIALS OF FORMAL LOGIC 

titious, as "a book considered twice as large as it is". 
Some factitious ideas may be partly arbitrary and 
partly discursive, as "the heroes of fiction". 

19. Ideas are also classified ACCORDING TO 
THE OBJECTS WHICH THEY REPRESENT. 
Now the objects of ideas may be considered either in 
their COMPREHENSION or EXTENSION. 

A. If we consider their comprehension, ideas are: 

SIMPLE and COMPOSITE. 

A simple idea is one that contains but one "note", 
and does not bear any further analysis, as the idea 
of "being". 

A composite idea contains two or more "notes" into 
which it can be resolved, as "tree", "house". 

(Care must be taken to distinguish a "simple idea" 
from a "simple being", nor must a "composite idea" be 
confounded with a "factitious idea". Find examples.) 
CONCRETE and ABSTRACT ideas. 

A concrete idea expresses a subject with a quality 
or "form", as "man", "red", "wise". 

An abstract idea expresses a quality or form without 
a subject, as "humanity", "redness", "wisdom". 

B. If we consider their extension, ideas are: 

SINGULAR, UNIVERSAL, PARTICULAR, 
COLLECTIVE, TRANSCENDENTAL. 

A SINGULAR idea expresses one and only one 
individual thing, as "President Wilson", "this man". 

(The "notes" that manifest the individual and which 
are called "individuating notes" are enumerated by the 
ancient logicians in the following verse : 

Forma, figura, locus, tempus, stirps, patria, nomen.) 

A UNIVERSAL idea expresses one or more "notes" 
which can be predicated in the same sense distribu- 
tively of many. As "man", "American", "white", 
"square". By "distributively" is meant that the com- 



CLASSIFICATION OF IDEAS 21 

prehension of the idea can be applied to each of the 
objects taken separately. The objects to which the 
universal idea can be applied are called the inferiors 
of the idea. 

A PARTICULAR idea is the same as a universal 
idea but restricted to some indeterminate part of its 
extension, as "some man", "certain poets". 

A COLLECTIVE idea is one that is applied to a 
group of objects taken as a whole, as "army", "family", 
"flock". It cannot be predicated distributively of each 
individual of the group. An idea that is collective 
from one point of view may be universal from another 
point of view, as "army" when applied to the armies 
of the different nations. 

A TRANSCENDENTAL idea expresses that which 
can be applied not merely to many, but to everything 
that can be thought of, as "being", "thing", "some- 
thing", "one", "true", "good". Transcendentals, as 
we shall afterwards see, are not strictly speaking 
universals. 

VARIOUS KINDS OF UNIVERSAL IDEAS 

Since man has the power to judge and reason be- 
cause his intellect forms universal ideas, it is of 
paramount importance to understand the different 
classes of those universal ideas. The brute beasts are 
incapable of forming universal concepts. Universal 
ideas are : 

DIRECT AND REFLEX. 

A DIRECT universal is a nature stripped by the 
power of abstraction of its individuating "notes" and 
affirmable of the subject from which it was abstracted, 
as "man" is affirmed of George Washington. It is the 
direct universal that is predicated in judgments. 



22 ESSENTIALS OF FORMAL LOGIC 

A REFLEX universal is this same nature, "man", 
for instance, which by an act of reflection upon the 
way it is conceived in the mind, is now discovered to 
apply to each and every man. The universal (uni- 
versus) is one thing towards which many are turned 
or united, but in such a way that this one thing is found 
to be multiplied in each of the many. The individuals 
to which the universal may be applied are called its 
inferiors. 

The direct is the universal of the "first intention", the 
reflex is the universal of the "second intention". The 
direct is a true universal, because, as a fact, it is a 
nature found or capable of being found in many, yet 
before the act of reflection upon the way this nature is 
conceived by the mind, it is not discovered as some- 
thing that exists or is capable of existing in many, and 
therefore not known to be a universal. 

A. DIVISIONS OF THE REFLEX UNIVERSALS 

The logicians have examined the various ways in 
which the things that are common to many are related 
to their inferiors, and they have found, as a result of 
their inquiry, that those relations fall under five different 
classes "called PREDICABLES, namely, SPECIES, 
GENUS, SPECIFIC DIFFERENCE, PROPERTY 
and ACCIDENT. So that whatever it may be that is 
common to many inferiors, is a species, genus, etc., 
of these inferiors. But since that which is common 
to many may be used as a predicate of each, we may 
define the PREDICABLES as the various relations in 
which predicates may stand to their subjects. 

A SPECIES is that which expresses the sum total 
of the essence of many individuals, as "man". An 
essence is that which constitutes a thing what it is. 



CLASSIFICATION OF IDEAS 23 

A GENUS is that part of the essence which is com- 
mon to other species, as "animal". 

A SPECIFIC DIFFERENCE is that part of the 
essence which marks off one species from others of the 
same genus, as "rational". The genus and specific 
difference together make up the species. 

A PROPERTY is that which, though it does not 
form part of the essence, yet necessarily flows, from 
the essence and is always connected with the essence, 
as the "power of laughter in man". 

An ACCIDENT is that which neither forms a part 
of an essence nor necessarily flows from an essence. 
It may be present or absent without affecting the 
essence, as "to walk", "to write poetry". 

THE PORPHYRIAN TREE. The various Pred- 
icates are well illustrated by the famous Tree of 
Porphyry. 

Substance 
Corporeal Incorporeal 

Body 
Animate Inanimate 

Living Being 
Sensible Insensible 

Animal 
Rational Irrational 

Man 
John Peter James 

The HIGHEST GENUS (substance) is that which 
is not subordinate to any higher genius. 

PROXIMATE GENUS is that under which a 
species is immediately contained, as "living being" 
with respect to "animal", "animal" with respect to 



24 ESSENTIALS OF FORMAL LOGIC 

A SUBALTERN GENUS is any genus which is a 
species of a higher genus, as "living being", "body". 

The LOWEST SPECIES (man) is that which has 
no other species beneath it. All other species above 
the lowest are called subaltern species. 

The Porphyrian Tree also illustrates the law of 
inverse ratio regarding the extension and compre- 
hension of universal ideas in the same field of thought. 



B. CLASSIFICATION OF THE DIRECT 
UNIVERSALS 

DIRECT UNIVERSAL IDEAS represent realities. 
A reality is something not created by the mind, but 
has some mode of existence independent of the mind, 
so that the mind by the act of knowing it, simply dis- 
covers what was already in existence. 

The reflex universal idea is the very same nature 
or thing as the direct universal, but now clothed with 
this added characteristic, namely, that which the direct 
universal idea represents is, or may be multiplied in 
many individuals. This characteristic "of one in 
many" the mind discovers by an act of reflection upon 
the direct universal idea combined with an act of 
comparison between what the idea represents and the 
many inferiors in which it is, or may be found. 

Now when we predicate, for instance, that John 
Smith is an American, we do not mean to say that 
John Smith possesses the attribute "American" that 
is common to many ; at least we do not ordinarily mean 
this. We mean rather that John Smith possesses an 
attribute, "American" — that is a reality, a fact with- 
out adverting at all to whether that reality is in John 
Smith alone or is shared by many others. 



CLASSIFICATION OF IDEAS Z5 

Hence what we predicate of a subject is some reality 
and therefore predicates are represented in the mind 
by the direct, not by the reflex universals. 

Now we ask the question, what are the highest classes 
into which all predicates, representative as they are of 
realities, are divided? We answer with Aristotle that 
they are divided into ten classes, called CATEGORIES 
or PREDICAMENTS, namely : 

SUBSTANCE, QUALITY, QUANTITY, RELA- 
TION, ACTION, PASSION, TIME, PLACE, 
POSTURE, HABIT. 

These are the ten aspects into which all reality is 
divided. They are the ten highest classes of realities 
which may be predicated of any subject. 

The Categories or Predicaments are therefore the 
highest classes into which all reality is divided. 

Take for example an individual named John Smith. 
You can say or predicate that 

John Smith is a rational being (man).. Substance 

" " fair-haired Quality 

" 5 ft. 10 inches high Quantity 

" "an American Relation 

" " working at accounts .... Action 

" fatigued Passion 

" " (fatigued) at 10 A. M.. . Time 

" at 42nd Street Place 

" seated at a desk Posture 

" " wearing a negligee shirt. Habit 
Any other predicate you may assert of John Smith will 
be found to fall under one or other of these heads. 

A SUBSTANCE is that which exists in itself and 
does not inhere in another as in its subject, as man, 
horse, tree. 

QUANTITY is the extension of a substance in 
space. 



26 ESSENTIALS OF FORMAL LOGIC 

QUALITY is some determination which charac- 
terizes a nature. 

RELATION is the order which holds between two 
things. 

PLACE is position in relation to surrounding space. 

TIME is position in relation to the course of events. 

POSTURE, the relative position of parts in the 
object itself. 

ACTION, the production of change in some other 
object. 

PASSION, the reception of change from some 
agent. 

HABIT is a determination which belongs to the 
integrity of the subject and equips it for its work. 
(Cf. Joyce.) 

CLASSIFICATION OF IDEAS ACCORDING TO 

THE PERFECTION WITH WHICH THEY 

REPRESENT THEIR OBJECTS 

20. CLEAR and OBSCURE— 

A CLEAR IDEA is one whose notes in kind and 
number are sufficient to distinguish its object from all 
other objects. 

An idea is OBSCURE when its notes are not suf- 
ficient to distinguish its object from others. 

CLEAR IDEAS are subdivided into DISTINCT 
and CONFUSED. 

A distinct idea is a clear idea, some notes, at least, 
of whose object we can distinguished from one another. 

A confused idea is a clear idea whose notes we can- 
not so distinguish from one another. 

Distinct ideas are also subdivided into complete and 
incomplete; complete when we can distinguish from 
one another all the characteristic notes of the object 
represented, incomplete when we cannot. 



CLASSIFICATION OF IDEAS 27 

A COMPREHENSIVE IDEA is one the knowl- 
edge of which exhausts all that can be possibly known 
of its object. Such knowledge is beyond the power of 
the human mind. Man's knowledge is limited. 

A PROPER IDEA is one that is directly derived 
from its object and thus directly represents its object 
without any further reference to another object. 

An ANALOGOUS IDEA is a proper idea with 
regard to the objects from which it is directly derived 
and represents, and applied to other objects because of 
some resemblance between them and its proper objects. 
Our concept of God is analogous. We draw from 
creatures around us ideas that represent Greatness, 
Power, Wisdom, Truth, Justice, Mercy, Love, Life, 
Joy, Happiness, etc. Removing from these all bounds 
we attribute them to God. These attributes in crea- 
tures are only faint resemblances to the same attributes 
in God. But since we cannot see God here face to 
face, but only as it were imperfectly mirrored in 
creatures, our concept of Him is only analogous. 

An ANALOGOUS IDEA represents its objects 
partly in the same and partly in different meanings, as 
the leg of an animal and the leg of a table. There is 
a certain resemblance between the leg of an animal and 
the leg of a table ; they are both supports, but there is 
also a difference, one is the support of an animate 
being, the other of an inanimate. 

CLASSIFICATION OF IDEAS ARISING 

FROM A COMPARISON WITH 

OTHER IDEAS 

21. Ideas when compared are COMPATIBLE and 
REPUGNANT. 
COMPATIBLE IDEAS are those which represent 



28 ESSENTIALS OF FORMAL LOGIC 

attributes which can co-exist in one and the same 
object, as "learning" and "prudence" in man. 

REPUGNANT IDEAS are those which represent 
notes that cannot co-exist in the same object, as a 
circular and a square figure. Repugnant ideas are 
called OPPOSITES. 

OPPOSITE ideas are those which represent notes 
that cannot, under the same respect, co-exist in the 
same thing. 

Opposite ideas are divided into four classes — contra- 
dictory, contrary, privative, and relative ideas. 

CONTRADICTORY ideas are those that represent 
any positive attribute or thing and its pure negation, 
as "man" and "not-man". The opposition between 
contradictory ideas is called contradictory opposition. 
Contradictory ideas, then, are those of which one sets 
forth the negation of the note or notes which the other 
asserts. Between contradictories there is no mean. 
Contradictories not only exclude each other, but they 
both include all things actual and possible. Everything, 
no matter what it be, whether it be matter or spirit, 
actual or possible, is either "man" or "not-man". 
Hence the greatest of all opposition exists between 
contradictories, because between them there is no 
medium. 

CONTRARY ideas are those which are farthest 
removed from each other among those which belong 
to the same genus, as "white" and "black", "sweet" 
and "sour", "virtue" and "vice". Between contraries 
there may be a mean or medium. They do not exhaust 
between them all things. The opposition between con- 
trary ideas is called contrary opposition. 

PRIVATIVE ideas represent a positive note and its 
negation or absence in an object in which it is capable 
of existing or naturally expected to exist, as "sight" 






CLASSIFICATION OF IDEAS 29 

and "blindness". You cannot attribute blindness to 
a stone or a tree, because its opposite, "sight", is not 
expected to exist in these objects. The opposition 
between privative ideas is called privative opposition. 

RELATIVE ideas are those that represent objects, 
one of which implies that there is another object con- 
nected with it, as "parent" and "child", "master" and 
"servant". The opposition between such ideas is called 
relative opposition. 

ASSOCIATED ideas are those which, when one 
arises in the mind, another is also aroused, as "my 
college" and my "fellow pupils" or "teachers", etc. 



Chapter III. 

The Outward Expression of Ideas 

22. Our ideas would remain hidden in our souls, did 
we not reveal them by outward "signs". We may 
make use of many kinds of signs to express our ideas, 
as gestures, laughter, sighs, etc., but the chief kind of 
signs we employ is called "Words". "Word" has 
less extension than "sign". We shall first treat of the 
meaning and classes of "signs", then the meaning and 
classes of "words". 

SIGNS 

DEFINITION— A SIGN is that through which 
one arrives at the knowledge of something else. 
Examples — A cloud, smoke, figure of an Indian, etc. 

DIVISION of signs — A. By reason of the way the 
sign signifies something it is either 

An OBJECTIVE sign (Signum ex quo), a sign 
which, when previously known, leads to the knowledge 
of something else, as "rainbow", "the footprints which 
Robinson Crusoe observed on the sand" ; or 

A FORMAL sign, i. e. a sign which, though not 
previously known, leads to the knowledge of some- 
thing else. It is called also "signum quo". An idea 
is such a sign. It manifests its object, but it is not 
itself manifested. Ideas do not as signs previously 
known represent objects but are forms determining the 
mind to perceive objects. Knowledge is the repro- 
duction in the mind of objective reality (cognito est 
similitude* rei) . The reproduced object in the mind is 
not the object we know. 

30 



THE OUTWARD EXPRESSION OF IDEAS 31 

B. By reason of the connection a sign has with the 
thing it signifies it is 

NATURAL, e. g. Cloud— smoke— idea. 
ARBITRARY or Conventional— "three golden 
balls", "the Stars and Stripes", "words". 

WORDS 

23. A WORD is an articulate sound uttered by the 
organs of speech. Words are arbitrary or conven- 
tional signs of ideals. They manifest ideas and are 
substitutes for things. Distinguish carefully between 
"words" and "signs" ; between "words" and "terms". 

A TERM in general is the expression of an idea. 
More precisely a term expresses the whole subject or 
the whole predicate of a proposition, as "industry-is- 
a-good-quality-in-a-student" ; "a", "good", "in", in 
this proposition are "words" but not "terms", "indus- 
try" is both a "word" and a "term". Hence some 
words are called Categorematic, those namely which of 
themselves can be used as a term, as "industry". 
Other words are called Syncategorematic , namely 
those that must enter (syn — with) with one or more 
categorematic words into the composition of a many- 
worded term, as articles, prepositions, conjunctions 
and interjections. What of the verb? The only verb 
logic recognizes is the verb "is" or "are". The re- 
maining part of other verbs is logically represented 
by a participle or a phrase, as "John loved" would be 
logically expressed — "John is one who loved". This 
will be explained more fully under Judgments and 
Propositions. 

TERMS 

24. The elements of a judgment are two "mental 
terms", and "the perception of their agreement or dif- 



38 ESSENTIALS OF FORMAL LOGIC 

ference"; the elements of a proposition are "two 
terms" and the "copula". Hence there are 

Mental terms — same as Ideas. 

Oral " — the idea as expressed by speech. 

Written " — the written expression of ideas. 
A term {terminus) is so called because the subject 
and predicate terminate or complete a proposition or 
judgment. 

DIVISION OF TERMS 

25. We have already set forth the divisions of mental 
terms or ideas. Generally speaking the divisions of 
ideas may also be employed as divisions of terms. 
The following divisions of terms call for special 
attention : 

UNIVOCAL AND EQUIVOCAL terms. An 
univocal term is one that is always employed in the 
same meaning or comprehension, as "animal" when 
said of "man" and "brute". 

An EQUIVOCAL term is one, which though spelled 
and pronounced alike, is yet employed in entirely dif- 
ferent meanings or comprehensions, as "bit", "box", 
"chest", "vice". The equivocation is in the word, not 
in the idea. There is no such thing as an equivocal 
idea. 

ANALOGOUS term. Analogy (dpaXoyla) means 
comparison or proportion. It is usually defined as a 
term whose meaning when applied to different objects 
is partly the same and partly different. We speak, for 
instance, of the "food of the body" and the "food of 
the soul". The meaning of food in both cases agrees 
in this, that it nourishes and strengthens, in one case 
the body, in another, the soul, yet it differs inasmuch 
as the food of the body is different in kind from the 
food of the soul. 



THE OUTWARD EXPRESSION OF IDEAS 33 

Analogy is intrinsic and extrinsic. 

INTRINSIC analogy is had when that which the 
analogous term expresses is found within or is intrinsic 
to the different objects to which it is applied, as 
"wisdom" when applied to "man" and to "God". 
Wisdom is found in man and in God, though in dif- 
ferent grades of perfection. In man "wisdom" is 
finite and dependent, in God infinite and independent. 

EXTRINSIC analogy is had when that which the 
analogous term expresses is in or intrinsic to one object 
and applied to others on account of some relation which 
the latter objects bear to the former, as "healthy" when 
applied to animal bodies, to food, climate, color, litera- 
ture. "Healthy" is said properly and primarily of an 
"animal body", because it is a quality in or intrinsic 
to an animal. But "healthy" is applied to food not 
because it is a quality primarily and properly of 
food, but because food causes health in an animal. 
"Health" as an effect of food is therefore something 
outside or extrinsic to the food. The grounds of 
extrinsic analogy are relations of cause and effect, 
similarity, resemblance, the relation of the container 
and the contained, as in the use of "healthy" when 
applied to food (cause), "laughing" when applied to 
water (similarity or resemblance to laughter, which 
properly belongs to the human countenance), "sweet" 
cup, (the sweetness of the liquid contained is trans- 
ferred to the cup which contains it). 

SUPPOSITION OF TERMS 

26. The supposition or use of a term (supponere, to 
stand for) signifies the meaning which is attached to 
it in a given case. 

A term may have a COLLECTIVE or DISTRIBU- 



34 ESSENTIALS OF FORMAL LOGIC 

TIVE use. Collective, when the term applies to a 
number of individuals taken as a group; Distributive, 
when the term applies to many individuals taken singly 
or separately, as "the citizens of New York built the 
Brooklyn bridge" (collective) "the citizens of New 
York elected a Democratic mayor" (distributive). 

REAL AND LOGICAL use. Real, when the term 
expresses an object as it is in itself, that is, inde- 
pendently of the mind, as "St. Paul" ; Logical, when it 
expresses a mode of existence which is found only in 
the mind, as "man" considered as a species. All the 
objects of "Second Intentions" are logical in their 
supposition. 

MATERIAL SUPPOSITION or use is had when 
the term is used to express itself as a spoken sound 
or a sign, as "Cicero is a word of three syllables"; 
"rattle" is a word whose sound expresses its sense, 
The supposition then of a term is nothing else but 
the meaning which the mind attributes to a certain 
term in any particular case. 



Part II 
THE SECOND ACT OF THE MIND— JUDGMENT 

Chapter I 
Nature of Judgment 

27. A Judgment is an act by which the mind 
perceives the agreement or disagreement between two 
objective ideas, or with St. Thomas, "an act of the 
intellect whereby the mind combines or separates two 
terms [meaning two objective mental terms] by 
affirmation or negation". 

EXPLANATION : "An act of the mind" expresses 
the "genus" of which judgment is a species, just as 
"animal" — in the definition of man — expresses the 
"genus" of which man is a species. 

"By which it perceives the agreement or disagree- 
ment of two objective ideas" is the "specific dif- 
ference" which distinguishes judgment from "simple 
apprehension". 

Because judgment is an "act of the mind", it is there- 
fore not three separate acts of the mind corresponding 
to subject, copula, and predicate, but one, single act. 

"Of two objective ideas" — The word "objective" is 
added to the definition because when the mind says, for 
instance, that "heat expands iron", the meaning is not, 
that the mere subjective act by which the mind knows 
heat agrees with the subjective act by which the mind 
knows "expands iron", but the meaning is that there 
is an objective agreement between "heat" and "a thing 
35 



36 ESSENTIALS OF FORMAL LOGIC 

that expands iron", that is, that something outside the 
mind is really so, as a fact. 

The essence of the judgment consists in one single 
flash of perception uniting or separating two objective 
ideas. 

The two objective ideas are the "matter" of the 
judgment, that is, that out of which the judgment is 
made. The "form" of the judgment or that which 
determines the "matter" to be a judgment and nothing 
else, is the perception of agreement or difference be- 
tween the ideas. A judgment therefore is "formally" 
one simple act, though "materially" a composite act. 

What expresses orally the matter? The subject and 
predicate terms. What is the expression of the "form" 
of a judgment? The words "is" or "is not", "am" or 
"am not", "art" or "art not", "are" and "are not". 

What, therefore, are the prerequisites of a judg- 
ment (that is, what is needed beforehand in order that 
a judgment may be formed) ? (1) Two objective 
ideas; (2) A comparison of these same ideas; 
(3) Then follows the act of judgment properly, so 
called, namely, the perception of the agreement or dis- 
agreement between these two objective ideas. 

What is the oral expression of a judgment called? 
Proposition. A proposition, therefore, is a group of 
words that express a judgment. And, just as two 
objective ideas, an act of comparison between them 
and the perception of their agreement or disagreement 
are the elements of a judgment, so the subject-term, 
the predicate-term and the verbally expressed copula 
are the elements of a proposition. 

The copula is in some judgments expressed ex- 
plicitly, as "Socrates is a man", in others the copula 
is only implicitly expressed, as "Socrates writes", 
which, in strictly logical form, is "Socrates-is-writing". 



NATURE OP JtJDGMENT 87 

DIVISIONS OF JUDGMENTS 

There are certain divisions which have reference to 
Judgments proper — that is, to Judgments as "acts of 
the mind". Afterwards we shall give the divisions that 
are common to both Judgments and Propositions. 

DIVISIONS OF JUDGMENT PROPER 

28. IMMEDIATE AND MEDIATE: An IM- 
MEDIATE judgment is one in which the agreement or 
disagreement of the subject and predicate is perceived 
without a middle term, or by the mere comparison of 
both, as "The whole is greater than its part" — "The 
sun shines". 

A MEDIATE judgment is one in which the agree- 
ment or disagreement of the subject and predicate is 
known by comparison of both with a middle term, as 
the "Three angles of a triangle are equal to two right 
angles". Briefly an "immediate judgment" is one that 
is formed without a process of reasoning ; a "mediate", 
through a process of reasoning. 

TRUE AND FALSE: TRUE, one that is in har- 
mony with reality : "God exists" ; FALSE, one that is 
not so, "a circle is not round". 

UNCERTAIN is one that expresses a doubt or 
an opinion ; CERTAIN is one that is uttered without 
any fear of error, as "Twice two are four"; an 
"opinion", if uttered with fear of error, as "Tomorrow 
will be rainy". 

PRUDENT and RASH : PRUDENT, which rests 
on serious, RASH, on trivial motives — Consult your 
experience for examples. 

A SYNTHETIC judgment is one, in which the 
agreement or disagreement of subject and predicate 



38 ESSENTIALS OF FORMAL LOGIC 

is known by experience alone — as "water extinguishes 
fire"; "fire burns". 

AN ANALYTIC judgment is one, in which either 
the predicate is contained in the comprehension of the 
subject, or the subject in the comprehension of the 
predicate, as (1) "A square has four sides" (2) "A tri- 
angle is a figure having its interior angles equal to 
two right angles". 

PROPOSITION 

29. A PROPOSITION is the oral or written ex- 
pression of a judgment. A judgment is an internal 
act of the mind ; a proposition is its external Sign. 

a) What therefore are the elements of a propo- 

sition? Define each. (27) 

b) What constitutes the matter, what the form 

of a proposition? (27) 

The copula in the logical proposition is always in the 
present tense and in the indicative mood. 

"Present tense", because though a judgment may be 
made about either past or future matter, yet that judg- 
ment is always made at the present moment. The 
expression therefore that corresponds to that present 
act of the mind must be in the present tense. 

"Indicative mood" — because if not in the indicative 
mood the copula would not express either truth or 
falsehood. And it is the purpose of Logic to direct 
the mind in the attainment of truth. 

It follows therefore that any other tense but the 
present, and any other mood but the indicative, belong 
to the predicate of the proposition, not to the copula. 
To reduce any proposition of other tenses and moods 
to a strictly logical form, change the verb to the appro- 
priate form of the verb "to be" and express its moods 



NATURE OF JUDGMENT d9 

or tenses with the predicate by other words. For 
example the logical form of the Proposition "He was 
my friend" is "He-is-one-who-was-my-friend" ; of 
"Peter will sin" is "Peter-is-a-future-sinner". 

In like manner a proposition of one word or two, as 
"Rain", or "It rains" or "He lives" may be expressed 
logically "Rain-is-falling", "Raining-is-a-fact", "He-is- 
living". We have colloquial expressions worded in 
this logical form, as "He is a-has-been", "He is a 
goner". The copula does not express the real or 
actual existence or non-existence of the terms, but 
merely the identity or non-identity of the terms. 
Predication therefore is the affirmation or negation of 
identity between two objects of thought. 

Exercise. Express in logical form the following: 
"John broke the window", "The sun may shine to- 
morrow", "John had seen me in New York yesterday", 
etc. 

Notice that in literary language the subject is not 
always first, — as "Blessed are the meek", "Great is 
Diana of the Ephesians". 

DIVISIONS OF PROPOSITIONS 

30. We may divide propositions according to two 
main principles — First, on account of something com- 
mon to all Propositions, namely their essential 
elements; secondly, by reason of something special 
to only a certain class of Propositions, namely the 
properties peculiar to this limited class. 

If we divide propositions by reason of something 
common to all, namely their essential elements, we may 
consider them 

A. By reason of the relation between Subject and 
Predicate or their Matter, or 



40 ESSENTIALS OF FORMAL LOGIC 

B. By Reason of the extension of the subject, or 
their Quantity, or 

C. By reason of the nature of the Copula, or their 
Quality. 

A. By reason of the relation between Subject and 
Predicate Propositions are: 

a. NECESSARY, when the predicate is neces- 

sarily related to the subject, that is, when 
the predicate is such that it springs from 
the essence of the subject, as "A circle is 
round". 

b. IMPOSSIBLE, if the predicate is repugnant 

to the subject, as "an angel is a man". 

c. CONTINGENT, when the predicate is actu- 

ally in the subject but may not be, as "John 
is a scholar". 

d. POSSIBLE, when the predicate is able to 

be, but actually is not in the subject — "The 

Philippines may be independent". 
Laws — All affirmative necessary propositions are 

true. 
All negative necessary propositions are false. 
All affirmative impossible propositions are 

false. 
All negative impossible propositions are true. 
All universal contingent propositions are 

for the most part false. 
All particular contingent propositions are 

true. 

B. By reason of quantity. 

The QUANTITY (quantum) of a proposition re- 
fers to the number of individuals to which the propo- 
sition refers. Hence the quantity of a proposition is 
determined or known by the extension of its subject. 

Now the extension of the subject may be — 



NATURE OP JUDGMENT 41 

A. SINGULAR. 

B. PARTICULAR. 

C. UNIVERSAL. 

D. INDEFINITE. 

So propositions are divided by reason of their exten- 
sion or quantity into : 

A. Singular, whose subject is a singular term, 

as "Peter is a Saint". 

B. Particular, whose subject is a particular 

term, as "Some men are learned". 

C. Universal, whose subject is a universal term, 

as "All men are mortal". 

D. Indefinite, whose subject is not determined 

by any sign of its extension, "Soldiers are 
greedy for glory". 
We have seen that a proposition is singular, uni- 
versal, particular or indefinite, when its subject is sin- 
gular, etc. The quantity of a proposition, therefore, 
depends upon the extension of its Subject. 

Now a Universal Proposition may be Universal in 
three ways. It may be : 

Metaphysically \ 
Physically v Universal 

Morally J 

A proposition is METAPHYSICALLY universal 
when it is such that it holds in all cases, so that no 
exception is possible even by the power of God, as 
"The whole is greater than any of its parts", "Man is 
a rational animal". These propositions are also called 
"absolute", "necessary", "a priori", "analytical". 

A PHYSICALLY Universal proposition is one 
which admits no exception in the order of nature, but 
may admit of an exception in the supernatural order, 
that is, through the power of God working a miracle, 
as "Fire burns". Propositions of this kind are also 



42 ESSENTIALS OF FORMAL LOGIC 

called Contingent, Hypothetical, a Posteriori, Syn- 
thetic. 

A MORALLY Universal proposition is one which 
is ordinarily true, yet may, with difficulty, have excep- 
tions, as "Mothers love their children". 

C. By reason of their FORM (copula) , propositions 
are affirmative or negative: Affirmative when the 
identity of the subject and predicate is affirmed; 
Negative when the identity of the subject and predicate 
is denied. 

Keep well in mind that in a negative proposition the 
negative "not" must be bound up with the copula, that 
is, form one piece with it. Should the negative be 
added, not to the copula, but to the predicate, the 
proposition would be affirmative, as "Man-is-not-a- 
brute", whereas, "Man-is not-a brute" is negative. 
Hence, "Rebellion-is-not to acknowledge the authority 
of lawful government" is an affirmative proposition. 
In the same way, if the negative affects the subject, 
but not the copula, the proposition is affirmative, as 
"He who does not gather with me scattereth". The 
negative particle need not necessarily stand between 
the subject and predicate, thus "No bird is a quad- 
ruped" is negative. It is sufficient that the negative 
may be construed with the copula. 

Hence mark you well, the Extension of the subject 
of a Proposition is referred to as its Quantity; the 
Form of a proposition, that is, its standing as affirma- 
tive or negative, is referred to as its Quality. 



Chapter II 
Laws That Regard the Extension of the Predicate 

31. The predicate of an affirmative proposition is 
always a Particular term, as "A horse is an animal" 
means not that "horse" can be applied to all and each 
inferior under the term "animal", but a horse can be 
applied to some only of the inferiors of animal. There 
are two important cases where this law is not true. 
One of these exceptional cases will appear in the chap- 
ter on Definition, another in Ontology. 

The predicate of a negative proposition is always 
a Universal Term, as "A man is not a tree", or "No 
man is a tree", the meaning is that "Man is not this 
or that or any other tree". Hence tree is denied of 
man Universally. 

Another way of expressing these laws is: "The 
Predicate of an affirmative proposition is not dis- 
tributed or taken Universally ; while the predicate of a 
negative proposition is always distributed or taken 
Universally". 

These laws are of the utmost importance, as you 
shall afterwards see. Considering both the quantity 
and quality of propositions, logicians have called for 
brevity's sake : 

UNIVERSAL affirmative propositions — 

A Propositions. 

UNIVERSAL negative propositions — 

E Propositions. 

PARTICULAR affirmative propositions — 

I Propositions. 

PARTICULAR negative propositions — 

O Propositions. 
43 



44 ESSENTIALS OF FORMAL LOGIC 

For the future, then, we shall use for brevity's 
sake, the letters A, E, I, O, instead of universal 
affirmative, etc. 

The laws or rules for the distribution of the two 
terms in a Judgment or proposition may be thus briefly 
expressed. In A only the subject is always distributed ; 
in E both the subject and predicate are always dis- 
tributed; in I, neither the subject or predicate is 
distributed ; in O, only the predicate is distributed. 

Reflect upon these rules, until they become perfectly 
familiar to you. 

OTHER DIVISIONS OF PROPOSITIONS 

38. Propositions are: Simple, Complex or Com- 
pound. 

A SIMPLE proposition is one which affirms or 
denies one predicate of one subject, as "God is charity", 
"Man is not a brute". 

A COMPLEX proposition is a simple proposition 
that has a complex term for the subject or predicate. 
By a complex term is understood a many-worded term 
that expresses not merely the nature of a thing denoted, 
but also one or more qualifications belonging to it, as 
"The tall man with a cane whom I met on the road 
very early this morning is blind on account of an 
accident that had befallen him ten years ago". Re- 
member, though a term may be grammatically complex, 
it still forms only one single logical term. For the 
logician it is simple. 

A COMPOUND proposition is one in which are 
joined together many simple propositions, as "A pious 
man does good and avoids evil". "Hearts, tongues, 
figures, scribes, bards, poets cannot speak, write, sing 
numbers of his love for Anthony". 



LAWS THAT REGARD EXISTENCE OF PREDICATE 45 

Now, compound propositions are divided into two 
classes: EXPLICIT (aperte compositi), those whose 
compound character is apparent from their grammati- 
cal construction, as the example above; IMPLICIT 
(occult e compositi), those whose grammatical structure 
does not manifest or make apparent their composite 
nature. These in English are called "Exponibles", as 
"God alone is eternal". 

EXPLICIT COMPOUND Propositions are: CO- 
PULATIVE "Life and death depend upon God". 
"Neither riches nor honors make one happy". 

ADVERSATIVE, when the parts are connected by 
the particles "but", "nevertheless", etc. : "The heavens 
and earth shall pass away but the word of God shall 
never pass away". "It is necessary that scandals come, 
nevertheless woe", etc. 

RELATIVE, when the parts are connected by 
"as — so", "where — there". "As you sow so shall you 
reap"; "Where charity abounds, there will happiness 
be". 

CAUSAL, when parts are connected by "for", 
"because", "since", etc. "Blessed are the meek, for 
(because) (since) they shall possess the land". 

CONDITIONAL OR HYPOTHETICAL, when 
introduced by "if". 

DISJUNCTIVE, when introduced by "either— 
or". Now, since there is really only one assertion in 
conditional and disjunctive propositions we may class 
them with simple. 

IMPLICIT COMPOUND Propositions are: 

EXCLUSIVE, as "God alone is eternal" ; i. e., "God 
is eternal and no other being is eternal". 

EXCEPTIVE, as "All but one perished" ; i. e., "One 
did not perish, and all others did". Exclusive and 
exceptive are practically the same. 



46 ESSENTIALS OF FORMAL LOGIC 

COMPARATIVE, as "Obedience is better than sac- 
rifice"; "Sacrifice is good, but obedience is better". 

REDUPLICATIVE, as "A man, inasmuch as he is 
an animal, feels". To perceive the full force of an 
"exponible" proposition, all that it implicitly implies 
ought to be explicitly stated. 



Chapter III 
Modal Propositions 

33. A MODAL proposition is one which asserts not 
only that the predicate is or is not in the subject, but 
also the way, mode, or manner in which the predicate 
is or is not in the subject, as "God is necessarily just". 
Modal are opposed to pure propositions. 

Whenever the copula is qualified by such words as 
necessarily, possibly, or by must, may, can, cannot, the 
proposition is modal. 

There are four kinds of ways or modes by which 
the subject may be connected with the predicate. 
Hence modal propositions are: 
NECESSARY 
CONTINGENT 
POSSIBLE 
IMPOSSIBLE 

Modal propositions may be reduced to simple propo- 
sitions, thus: 

S must be P=S is necessarily P or, that S is P is 
a necessity. 

S cannot be P=That S be P is an impossibility. 

S may be P=That S be P is a possibility, etc. 



47 



Chapter IV 

Relative Properties of Propositions 

34. We have already spoken of such properties as 
belong to propositions whether you think of other 
propositions or not, such as quality and quantity, etc. 
Hence they are called absolute properties. Relative 
properties belong to propositions when compared with 
one another. There are three kinds of properties 
which belong to propositions when compared one with 
another: opposition, cequipollence or equivalence (ceqm- 
polleatia), and conversion. 

OPPOSITION 

OPPOSITE propositions are in a wide sense those 
that have the same subject and predicate and differ in 
quantity or quality or in both. 

Opposition is in a more restricted sense the affirma- 
tion and negation of the same predicate regarding the 
same subject at the same time and under the same 
respect. 

What then are the three requisite conditions in order 
that propositions be opposed ? 

There are four species of opposition : 
(a) Contradictory (b) Contrary, 
(c) Sub-contrary (d) Sub-altern. 

CONTRADICTORY PROPOSITIONS are those 
which, having the same subject and predicate, differ 
both in quantity and quality. 

CONTRARY PROPOSITIONS are those which, 
having the same subject and predicate, differ in quality 
alone. 

48 



RELATIVE PROPERTIES OF PROPOSITIONS 49 

SUB-CONTRARY PROPOSITIONS are two 
particular propositions which, having the same subject 
and predicate, differ in quality. 

SUB-ALTERN PROPOSITIONS are those which, 
having the same subject and predicate, differ in quantity 
alone. The following diagram explains at a glance the 
different kinds of opposition. 

All S^is P Contrar y No S E is P 



C 



°*» «** 










J* 



Some S is P Sub-Contrary w s ° is not p 

LAWS OF OPPOSITION : 

(a) Contradictories cannot be at the same time true, 
nor at the same time false. 

(b) Contraries cannot be at the same time true, but 
they may be at the same time false. 

(c) Sub-contraries may be at the same time true, 
but cannot be at the same time false. 

(d) Sub-alterns can be at the same time true and 
at the same time false. 

Prove each of these laws. 

yEQUIPOLLENCE or EQUIVALENCE 
or OBVERSION 
1. Definition : 

^EQUIPOLLENCE is the reduction of two oppo- 
site propositions to the same signification by the use 
of the negative particle. 



50 ESSENTIALS OF FORMAL LOGIC 

Thus— 

S a P All men are mortal=No men are 

not-mortal. S e P 

S o P No philosophers are practical=All 

philosophers are not-practical. S a P 
S i P Some judges are just=Some 

judges are not not- just. S o P 

S o P Some ministers are not wise=Some 

t, . ministers are not-wise. S i P* 

Rule. 

Change the quality of the proposition and substitute 

for the predicate its contradictory term. 

THE CONVERSION OF PROPOSITIONS 

35. The conversion of propositions means the chang- 
ing of subject into the predicate and predicate into the 
subject without changing the meaning. 

Conversion is either: 

a. SIMPLE, when the quantity is preserved. 

b. ACCIDENTAL, when the quantity is not 

preserved. 

c. By CONTRAPOSITION we mean the con- 

version that is applicable to O and A. To 
obtain the contrapositive, first equipollate 
or obvert and then convert the proposition. 
Rule for the Conversion of propositions : 
Simpliciter /Eel convertitur; Et/A per acci. 
AstO per contra; sit fit conversio tota. 
The original proposition is called the "Convertend" ; 
the proposition that results from Conversion, the 
"Converse". 



Part III 

THIRD ACT OF THE MIND OR INTELLECT- 
REASONING 



Chapter I 
Nature of the Act of Reasoning 

36. Just as in the case of simple apprehension and 
term, judgment and proposition, so also we may con- 
sider the act of the mind in reasoning- and the expres- 
sion of that act. Like judgment, reasoning is an act 
by which the mind perceives the agreement or dis- 
agreement between two objective ideas, but it differs 
from judgment in this, that in reasoning the mind 
perceives the agreement or disagreement between two 
ideas through the medium of a third idea, whereas in 
a judgment proper the mind perceives the agreement 
or the disagreement between two ideas without the aid 
of a third idea. 

In other words Judgment in the ordinary sense is 
an act of immediate perception ; Reasoning is an act of 
mediate perception of the agreement or difference 
between two ideas. 

Every act of reasoning, therefore, is a judgment, 
though mediate; but every judgment is not an act of 
reasoning, because a judgment may be immediate. 

PREREQUISITES OF THE ACT OF REASON- 
ING — Just as the act of immediate judgment had its 
prerequisites (recall them) so also has the act of 
reasoning its prerequisites, namely: 
51 



52 ESSENTIALS OF FORMAL LOGIC 

a. Three ideas. 

b. The comparison of two of the ideas with 

the third. 

c. The perception of the agreement or disagree- 

ment between these two ideas and the third 
idea, in other words the formation of two 
judgments. 

d. Lastly, the perception of the agreement or 

disagreement of the two ideas, thus com- 
pared with the third, between themselves. 
This is precisely and formally the act of 
reasoning. 
We may therefore define the act of reasoning thus : 
"Reasoning is that act of the mind (intellect) by which 
the agreement or disagreement of two ideas is per- 
ceived through a comparison between them and a third 
idea". 

QUESTION— What, therefore, is the remote matter 
of reasoning; what is the proximate matter; what is 
the form of reasoning? 

The laws of thought on which the act of reasoning 
rests are: 

a. The law of IDENTITY or AGREEMENT. 
Things that are identical with the same thing are 
identical with one another. This principle is self- 
evident and cannot itself be proved. It needs no proof. 
This is the principle on which rests every affirmative 
conclusion in reasoning. 

b. The law of DISAGREEMENT or DIFFER- 
ENCE. Tzvo things, one of which agrees with a third 
thing, and the other of which disagrees with the same 
third thing, disagree with each other. This is also 
self-evident, and needs no proof, nor can it be proved. 
It is the principle on which rest all negative con- 
clusions in reasoning. 



NATURE OF THE ACT OF REASONING 53 

Both these principles may be reduced to one, namely, 
to the principle of Contradiction, which is stated thus: 
"The same thing cannot be affirmed and denied of the 
same thing at the same time, and under the same 
respect". 



Chapter II 

The Expression of the Act of Reasoning 

37. The sign or the expression of the Act of Reason- 
ing is called an argumentation or Syllogism (thinking 
together). It is denned thus: A syllogism or argu- 
mentation is an inference by which, from two propo- 
sitions a new proposition is derived, the truth of which 
follows from these two as a necessary consequence. 

TECHNICAL TERMS INVOLVED IN A 
SYLLOGISM 

First regarding the terms contained in the syllogism 

a. There are three terms: Minor, Major, 

Middle. 

b. The Minor term is the S ; the Major, the P 

of the Conclusion. 

c. The Middle term is the term employed as a 

means or medium of comparison between 
the Minor and Major. 

d. The Middle term is repeated twice. 

e. These three terms constitute the Remote 

Matter of the syllogism. 
Secondly, regarding the propositions of the Syl- 
logism 

a. There are three propositions. 

b. The first two are called the premises, the last 

is called the conclusion. One premise is 
the Major, the other premise the Minor. 

c. The Major premise contains the Major term. 

It gives the relation between the Major 
and Middle terms. 
64 



THE EXPRESSION OF THE ACT OF REASONING 55 

d. The Minor premise contains the Minor term. 

It gives the relation between the Minor 
and Middle terms. 

e. The Major and Minor premises taken to- 

gether are called the antecedent. The con- 
clusion is called the consequent. 

f. The truth of the conclusion is therefore 

conditional because the truth of the con- 
clusion of a syllogism depends upon the 
truth of both premises. 

g. The Consequence (consequentia) is the con- 

nection in thought {nexus) between the 
Major and Minor premises. Its sign or 
expression is "therefore". 

h. The three propositions are the proximate 
"matter" of the syllogism. The "form" is 
the connection between both. 
Note — The "form" is the same as the "Conse- 
quence". 

The number of terms is not to be judged by the 
number of words. Many words can form 
one term. 

The syllogism is said TO BE IN FORM, when 
the premises are properly arranged for the 
purpose of drawing the conclusion. 

The conclusion is said to be "virtually" con- 
tained in the premises, that is, the con- 
clusion does not actually exist in the 
premises, but the premises have the power 
of producing it. The premises are also 
said to contain the conclusion implicitly 
but not explicitly. 

We are now treating of what is called the 
Categorical Syllogism, that is, one that is 
made up of categorical propositions. A 



56 ESSENTIALS OF FORMAL LOGIC 

categorical proposition is one that affirms 
or denies absolutely the agreement or dis- 
agreement of the subject and predicate. 
It is opposed to Conditional or Hypotheti- 
cal Syllogisms and also to Disjunctive Syl- 
logisms. 



Chapter III 

Rules of the Syllogism 

38 — 1. There must be three and only three terms : 
the Major,' Middle and Minor. 

2. No term must be distributed in the conclusion, 
which is not distributed in the premises. 

3. The Middle term must never be found in the con- 
clusion. 

4. The Middle term must be distributed in one, at 
least, of the premises. 

5. Two affirmative premises can never give a nega- 
tive conclusion. 

6. No conclusion can be drawn when both premises 
are negative. 

7. If one of the premises is particular the conclusion 
must be particular ; and if one of the premises is nega- 
tive, the conclusion must be negative. 

8. From two particular premises no conclusion 
follows. 

NOTE: Of these rules No. 1 and No. 3 refer to 
the structure of the syllogism; No. 2 and No. 4 refer 
to its quantity; No. 5 and No. 6 refer to its quality; 
No. 7 refers to quantity and quality. 

PROOF OF THE RULES 

39. Rule 1. From the nature of the act of reasoning 
the syllogism must have three terms, because when we 
cannot perceive the agreement or disagreement between 
two terms, we must have recourse to a third as a means 
(medium) of comparison. We cannot have four 
terms, because then there could be no comparison. 
57 



58 ESSENTIALS OF FORMAL LOGIC 

To secure three and only three terms, each term 
must be uni vocal. If any term is equivocal or am- 
biguous then there are really more than three terms. 
Examples of syllogism with equivocal terms: 

All chests are boxes, Man is a species, 

A part of me is a chest, Socrates is a man, 

. • .A part of me is a box, . * .Socrates is a species. 

In both Syllogisms is the fallacy called "Ambiguous 
Middle". 

Rule 2. Should the conclusion be wider than the 
premises, then there are really four terms — three in 
the premises, while the excess of extension found in 
the conclusion amounts to a fourth term — and this 
excess in the extension of the conclusion was not com- 
pared in the premises with the Middle term. 
Examples: 

All "Pierce-Arrows" are automobiles. 

A "Ford" is not a "Pierce-Arrow". 

. • . A "Ford" is not an automobile. 

This fallacy is called the "Illicit process of the 
Major" or the "Illicit process of the Minor". 

Rule 3. First, because the office of the Middle term is 
to serve as a means of comparing the Minor and Major 
of the conclusion. Hence it does not belong to the 
conclusion. 

Secondly, the conclusion contains the result of the 
comparison between the Minor and Major. That result 
therefore has to do with the Minor and Major, not 
Middle. The Middle is the means of arriving at the 
result, not the result itself. Therefore it is outside 
that result, and hence has no place in the conclusion. 
Examples: 

Cicero is an orator. 

Cicero is a Roman. 

.: . Cicero is a Roman orator. , , 



RULES OF THE SYLLOGISM 59 

Rule 4. Unless the Middle term is distributed at least 
once you may have four terms. Because if the Middle 
term is taken particularly twice, one of the extremes 
may be compared with the Middle term in one part of 
the latter's extension and the other extreme with 
another and different part of the extension of the 
Middle term. 
Examples: 

All crocodiles are animals. 
All men are animals. 

. • .All men are crocodiles. 

All queens are women. 
All female cooks are women. 
. • All female cooks are queens. 
This fallacy is called — "Undistributed Middle". 
Rule 5. It is impossible for two terms (Minor and 
Major) to agree with the third (Middle) and disagree 
between themselves. Yet a negative conclusion would 
demand such an impossibility. 
Example: 

All birds lay eggs. 
The ostrich is a bird. 
. • . The ostrich does not lay eggs. — This conclusion 
is absurd. 

Rule 6. Because, when both premises are negative, 
it is impossible to have any comparison between the ex- 
tremes (Minor and Major) and the Middle term. For 
the extremes cannot be connected with the Middle in 
any one of the premises. 
Example: 

Philosophers are not elephants. 
Socrates is not an elephant. 
. • .Socrates is not a philosopher. 
Rule 7. If one or other of the premises is negative, 



60 ESSENTIALS OF FORMAL LOGIC 

the conclusion must be negative. For when one ex- 
treme is identical with the Middle term, and the other 
extreme disagrees with the Middle term then the ex- 
tremes must disagree with each other. This disagree- 
ment can be expressed in the conclusion only by a 
negative proposition. 

If both premises are affirmative and one is particular, 
they both distribute but one term between them. This 
distributed term must be the Middle term. But the 
Middle term cannot be in the conclusion. Therefore 
there is nothing left for the conclusion but two undis- 
tributed terms. And a conclusion with two undistributed 
terms must be a particular. 

Rule 8. If both premises are particular affirmative, 
no term in these premises can be distributed. 

If one premise is affirmative and the other negative, 
they both have only one distributed term. But since 
the conclusion must be negative (Rule 7) two dis- 
tributed terms would be needed in the premises. 
Therefore, since there are not two, nothing can follow. 



Chapter IV 

Moods and Figures of the Syllogism 

40. MOOD — Definition. A "Mood" is the arrange- 
ment of the premises by reason of their quality and 
quantity. 

The propositions that make up the premises of every 
categorical syllogism are the typical propositional 
forms, A, E, I, O. Since there are but two premises, 
and each of these must be one of the four propositions 
A, E, I, O, it follows that there are but sixteen possible 
arrangements of premises, thus : 

AA EA IA OA 

AE EE IE -OE 

AI EI . II OI 

AO EO IO OO 
All these combinations cannot be employed as prem- 
ises of a syllogism. If we examine each of these 
combinations under the light of the Rules of the 
Syllogism, some will be found to be illegitmate. Thus : 

a. EE, EO, OE, OO have two negative prem- 

ises, and must be rejected by Rule Six. 

b. II, IO, OI, OO have two particular premises, 

and must be rejected by Rule Eight. 

c. IE — This involves an illicit process of the 

Major term. For the conclusion must be 
negative (Rule Seven). The predicate of 
this negative conclusion must be dis- 
tributed. This necessitates that the Major 
term should be distributed in its premise. 
But it is not. For I does not distribute 
any of its terms. Therefore a conclusion 
61 



62 ESSENTIALS OF FORMAL LOGIC 

drawn from IE must be vitiated by an 
illicit process of the Major. Therefore 
the mood IE must be rejected. A valid 
conclusion may be inferred from IE, but 
such an inference would not be drawn in 
the ordinary way. 
The possible moods therefore are eight in number, 

one combination of EI, and seven combinations which 

contain the premise A. 

FIGURES 

41. We must now examine which of these combina- 
tions or "moods" may be employed in the several 
Figures. 

FIGURES OF THE SYLLOGISM— Definition: A 
"Figure" is a form of the syllogism, determined by the 
position of the Middle term in the two premises. There 
are only four possible positions, hence four figures. 
They are : 

Figure 1. Figure 2. Figure 3. Figure 4. 
M. P. P. M. M. P. P. M. 
S. M. S. M. M. S. M. S. 



S. P. S. P. S. P. S. P. 

There are special rules for each figure: 
Fig. 1) a. The Minor premises must be affirmative. 

b. The Major premises must be universal. 
Fig. 2) a. One premise must be negative. 

b. The Major premise must be universal. 
Fig. 3) a. The Minor premise must be affirmative. 

b. The conclusion must be particular. 
Fig. 4) a. If the Major is affirmative, the Minor 
must be universal. 
b. If the Minor is affirmative, the conclusion 
must be particular. 



MOODS AND FIGURES OF THE SYLLOGISM 63 

c. If the conclusion is negative, the Major 
must be universal. 
In the light of these rules of the figures, you can 
discover the "moods" that are valid for each figure. 
These "moods" will be found to be nineteen. They 
are enumerated in the following mnemonic lines : 
Barbara, Celarent, Darii, Ferioque, prioris. 
Cesare, Camestres, Festino, Baroco, secundae. 
Tertia, Darapti, Disamis, Datisi, Felapton, 
Bocardo, Ferison, habet; Quarta insuper addit. 
Bramantip, Camenes, Dimaris, Fesapo, Fre- 
sison. 
The reason why we have only a certain number and 
certain kinds of moods in each figure : 
Figure I. 
Rule 1. Excludes AE, AO. Rule 2. Excludes IA, 
OA. Therefore four remain available for the First 
Figure: 

AA EA AI EI. 
Hence the mnemonics "Barbara, etc". 

Figure II. 
In this figure Rule 1, excludes AA AI IA. 

Rule 2, excludes IA OA. 
Hence the available moods are EA AE EI AO. 
Hence "Cesare, etc.". 

Figure III. 
Hence the valid moods in this are AA IA AI EA 

OAEI. 
Hence "Darapti, etc.". 

Figure IV. 
There are five valid moods, AA AE I A EA EE. 
Hence "Bramantip, etc.". 



Chapter V 
Reduction 

42. Aristotle held that only in the first figure is the 
validity of our conclusion absolutely evident. The first 
figure is perfect; the others, though valid, imperfect. 
The moods in the other figures are manifestly con- 
clusive when they are reduced to the form of the first 
figure. 

REDUCTION is defined as the process by which a 
syllogism in one of the other figures is expressed as 
a syllogism of the first. 

Now the names of the various moods, as given in 
the mnemonic lines are so ingeniously constructed as 
(1) to indicate the moods of the first figure, to which 
the moods of the other figures may be reduced ; and (2) 
what logical operations are necessary to achieve the 
result. 

( 1 ) Every mood begins with one of the letters B, C, 
D, F. These letters indicate respectively the mood of 
the first figure to which each is to be reduced. Thus 
"Cesare" to "Celarent, etc.". 

(2) Of the consonants composing the body of each 
word, the letters s, p, m, c are employed. These let- 
ters tell us what logical changes are required to obtain 
a syllogism in one of the moods of the First Figure. 
s) = (simpliciter — simple conversion) . It means that 
the premises indicated by the preceding vowel must be 
converted "simply". 

p) = (per accidens). That the premise preceding it 
must be converted "per accidens". 

m)=(muta, change). That the premises are to be 
transposed. 

64 



REDUCTION 65 

c) = (contradictory proposition). Indicates that the 
reduction is to be indirect or "per impossible". 

Now proceed to the operation of Reduction. 

The process which gives us a syllogism in the first 
figure precisely equivalent to the original syllogism 
is termed Direct or Ostensive Reduction. This kind 
of reduction presents no great difficulty. 

There are, however, two moods, Baroco Figure 2, 
and Bocardo Figure 3, to which the Direct or Osten- 
sive Reduction cannot be applied. To reduce these 
moods the Indirect Method of Reduction must be 
applied. 

This consists in admitting by way of hypothesis that 
the conclusion of the mood may be false, and in show- 
ing* by a syllogism in Barbara that this supposition 
involves the falsity of one of the original propositions. 
The original propositions are, however, known to be 
true. Hence we are forced to admit the conclusion 
in Bocardo and Baroco valid. 

Take the following Syllogism in Baroco : 
All whales are aquatic animals. 
Some mammals are not aquatic animals. 

.-.Some mammals are not whales. 

If the conclusion is false the contradictory must be 
true "All mammals are whales". 

We now use this proposition and one of the original 
premises to form a syllogism in Barbara — thus : 
All whales are aquatic animals. 
But all mammals are whales. 

. • .All mammals are aquatic animals. 

Now this conclusion is the Contradictory of one 
of the original premises: "Some mammals are not 
aquatic animals". This last by supposition is true. 
Therefore the conclusion arrived at in the second 
syllogism is false. But the error does not lie in the 



66 ESSENTIALS OF FORMAL LOGIC 

reasoning, for this is the first figure. The error must 
lie, therefore, in the fact that one of the premises of 
the last syllogism is false. The premise "all whales 
are aquatic animals" is, however, given as true. There- 
fore the error crept in by supposing "all mammals are 
whales" to be true. It is therefore false and the con- 
tradictory must be true — the original conclusion of 
Baroco. 

This "Indirect" Method of Reduction may be applied 
to any Mood, in place of the Ostensive Method. 



Chapter VI 
Hypothetical Syllogisms 

43. A HYPOTHETICAL SYLLOGISM is one 
whose Major premise is a hypothetical, and whose 
Minor is a categorical proposition. The Major fur- 
nishes the ground for the inference, while the Minor 
states a case in which the Major is applicable. 

LAW GOVERNING THE HYPOTHETICAL 
SYLLOGISM. The truth of the consequent follows 
from the truth of the antecedent, and the falsehood of 
the antecedent follows from the falsehood of the con- 
sequent. 

Rules of the Hypothetical Syllogism, — Only two 
(1) To posit the antecedent is to posit the consequent, 
and (2) to sublate the consequent is to sublate the 
antecedent. 

Hence only two moods. 

(1) The Constructive — as, If A. is B., C. is D. 

But A. is B. 
.-. C. isD. 

(2) The Destructive —as, If A. is B., C. is D. 

But C. is not D. 
. • . A. is not B. 
Hence there are two fallacies to which these syl- 
logisms are liable, namely 

(1) The fallacy of denying the antecedent. 

(2) The fallacy of affirming the consequent. 
Examples: 

(1) If icebergs are approaching our Atlantic sea- 
board we shall have cold weather. 

But icebergs are not approaching our Atlantic sea- 
board. 

. • . We shall not have cold weather. 
67 



68 ESSENTIALS OF FORMAL LOGIC 

This conclusion does not follow. 

(2) If Samuel's real estate depreciates in value he 
will be bankrupt. 

But he will be bankrupt. 

. ■ . Samuel's real estate depreciates in value. 

This conclusion does not follow. 

Of course you can have a purely hypothetical 
syllogism, that is, one in which the major and minor 
premises as well as the conclusion are hypothetical 
propositions, as 

If C. is D., E. is F. 
If A. is B., C. is D. 
. • . If A. is B., E. is F. 

Attempts have been made to reduce Hypothetical 
Syllogisms to a Categorical form, but such a process 
would not be a Reduction properly so called. 



Chapter VII 

The Disjunctive Syllogism 

44. Definition. A DISJUNCTIVE SYLLOGISM 
is one in which the major premise is a disjunctive 
proposition, and the minor a categorical proposition, 
either affirming or denying one or more members of 
the opposition. 
It has two moods. 

1. Modus ponendo tollens, as 
S is either P or Q. 
But S is P. 
. • . S is not Q. 
3. Modus tollendo ponens, as 
S is either P or Q. 
But S is not P. 
.-.SisQ. 
RULES: (1) To affirm one or more alternatives is 
to deny the remaining alternatives. (2) To deny one 
or more alternatives is to affirm the remaining alterna- 
tives. 

FALLACIES: (1) Care should be taken that the 

disjunctive should exhaust all the alternatives of the 

case, in other words that the disjunctive should be 

complete. For example: 

John is either in the Law or Medical department of 

Fordham University. 
But he is not in the Law department. 
. • . He is in the Medical department. He may be in 

the Collegiate department. 
(2) The alternatives should be mutually exclusive. 
For example : 
John is either in Fordham University, or in the Col- 
legiate, Law or Medical department. 
69 



70 ESSENTIALS OF FORMAL LOGIC 

But John is in Fordham University. 
. • . John is not in the Collegiate, Law or Medical 
department. This conclusion does not follow. 

Criticise the following arguments : 
John is either sleeping or not sleeping. 
But John is sleeping. 
. • . John is not sleeping. 

John cannot walk and be seated at the same time. 
But John is not at present seated. 
. • . John is walking. 



Chapter VIII 
Abridged and Conjoined Syllogisms 

45. Fully expressed syllogisms are rare in conversa- 
tion, in oratory, in argumentative literature. What is 
usual in practice is the use of imperfectly stated syl- 
logisms, either simple or complex. 

SIMPLE ABRIDGED SYLLOGISMS 

The Enthymeme — ( iv-Ovtfs ) is a form of argument 
in which the major or the minor or the conclusion is 
not expressed. One of the premises or the conclusion 
is suppressed or kept in the mind. 

Examples: Major premise omitted — 
"He is a coward for he is a liar". 

Minor premise omitted — 

"He is a coward for all liars are cowards". 

An enthymeme need not be categorical. It may 
also be pure hypothetical or pure disjunctive or any 
mixture of these various forms. Examples : "If crime 
is rampant the police of the city is not good ; for daring 
and reckless criminals are always in the minority". 
"Were he a child of Adam, he would do the works 

of Adam ; which he does not". 
"Our vicious propensities are such that we must 
either fall into sin and misery or practice self- 
denial". 
The enthymeme may easily become a cover for a 
fallacy. Certain principles not universally true, others 
not scientifically proved are adopted by certain classes 
of people as if they were really universal and acknowl- 

n 



78 ESSENTIALS OF FORMAL LOGIC 

edged by all scientists as true, and these certain classes 
who hold these principles reject any statement as false 
which may contradict their spurious principles. 
Examples: 

"He is a Catholic, therefore he is not a good Ameri- 
can citizen". 
"He is poor, therefore he is degraded". 
"He cannot read or write, therefore he cannot make 

a good citizen". 
"He is a student of Richdale, etc., therefore he is 

a refined gentleman". 
"He is an Englishman, therefore he is a noble char- 
acter". 
"He is a Jesuit, therefore he is a sly intriguer". 
"He is Irish, therefore he is not worth much". 
"Catholics do not admit complete evolution, there- 
fore they are wrong". 
"He belongs to the Hebrew race, therefore he must 

be persecuted". 
"He is a Catholic, therefore he is intolerant". 
"Divorce is an assertion of freedom, therefore it is 

right". 
REASONING BASED on principles generally but 
not universally true is subject to the same fallacy — 
such as "tramps are not to be trusted". 

Epicheireme — An argument to one or both of whose 
premises is an annexed reason to support it, as : 
Whatever is spiritual is immortal; for it is in- 
capable of corruption. 
But the human soul is spiritual. 
. • . The human soul is immortal. 
This form of reasoning is commonly used by orators. 
It may be drawn out into an ordinary syllogism, as : 
Whatever is incapable of corruption is immortal 
But whatever is spiritual is incapable of corruption. 



ABRIDGED AND CONJOINED SYLLOGISMS TS 

. • . Whatever is spiritual is immortal. 

But the human soul is spiritual. 
. • . The human soul is immortal. 
Sorites — An argument in the first figure with many 
Middle terms. It is based on the principle of the 
"dictum de omni", as: 

Socrates is a man. 
All men are mammals. 
All mammals are animals. 
All animals are living creatures. 
All living creatures are substances. 
. * . Socrates is a substance. 
This form of argument may be expressed in as many 
syllogisms as there are middle terms in the sorites. 

THE DILEMMA 

46. The Dilemma (the horned syllogism) whose 
Major is a disjunctive proposition containing two 
members, about each of which something contrary to 
our adversary is proved. 

Hence it is plain what Trilemma and Quadrilemma 
are. 

There are four kinds of dilemmas : 

A. Simple constructive, where there are two or more 
antecedents in the Major premise, and one consequent. 
In the constructive dilemma, the Minor is an affirmative 
disjunctive. 

Example: If I go out, I catch a cold; if I stay in, I 
catch a cold. 
But I either go out, or stay in. 
. • . I catch a cold. 

B. Complex constructive where there are several 
antecedents and several consequents. The Minor is 
again an affirmative conjunctive. 



W ESSENTIALS OF FORMAL LOGIC 

Example: If education is popular, compulsion is 
unnecessary. 
If unpopular, compulsion will not be 

tolerated. 
But education is either popular or un- 
popular. 
. • . Either compulsion is unnecessary or 
will not be tolerated. 
C. Destructive — where there are several antecedents 
in Major, and a negative disjunctive in the Minor. 
Example : If this man were wise, he would not abuse 
the Bible in jest; if he were good, he 
would not do so in earnest; but either 
he does it in jest or in earnest. 
. • . He is not wise or not good. 
The dilemma is of great value to the orator. 
Rules: (1) The enumeration of the alternatives 
should be complete and mutually exclusive. 

(2) See to it that your dilemma cannot be retorted 
by your adversary. A dilemma is retorted by showing 
that whichever alternative is chosen the conclusion 
opposite to yours may logically follow. 

(3) A dilemma may hide many fallacies. In order 
to detect them, reduce the dilemma to syllogistic form. 



Chapter IX 
Induction 

47. So far we have been dealing with deductive 
reasoning. In brief, deduction is a reasoning from 
the universal, to a less universal, to the particular, or 
to the individual, from what is true, of "all" to what is 
true of "some", or one. Its starting point is a general 
principle. 

In order, then, to reason deductively at all, it is plain 
that the mind must previously have arrived at the 
knowledge of universal truths, judgments, or propo- 
sitions. 

The important question to be now answered is : How 
do we arrive at the knowledge of universal truths, 
judgments or propositions? 

Before answering this question let us recall that 
every universal judgment is either immediately or 
mediately ANALYTIC or SYNTHETIC. 

IMMEDIATE ANALYTIC UNIVERSAL JUDG- 
MENTS. Examples of such judgments are: "The 
whole is greater than any of its parts"; "Every- 
thing that happens must have a cause". A little reflec- 
tion will enable us to discover that we arrive at the 
knowledge of immediate analytic universal judgments, 
not by a process of reason, but by the immediate mental 
processes of (1) observation, (2) abstraction, (3) gen- 
eralization, by which we reach the universal concept 
of their subjects and predicates, between which, by 
the processes of comparison and analysis, the mind 
intuitively perceives a necessary connection. Take the 
judgment : "The whole is greater than any of its parts". 
T5 



76 ESSENTIALS OF FORMAL LOGIC 

In the first place, by a simple act of observation, 
we come to know, let us say, this individual whole 
orange, and this individual part of it. 

By abstraction we may neglect the individuating 
notes of "this orange" and "this part of it", and by 
generalization, form the universal concepts — "whole" 
and "part", which may apply to any "whole" and 
"part". 

Then we compare and analyse the concepts 
"whole" and "part" of any object. The outcome of 
this comparative analysis will be an immediate, in- 
tuitive, universal and necessary judgment — "The whole 
(every whole) is greater than any of its parts". The 
necessary connection of the subject and predicate is 
based upon the simple comparative analysis of the 
nature of "whole" and "greater than any part". This 
process of forming immediate, universal, analytic 
judgments may be called, in a wide sense, Induction. 

MEDIATE ANALYTIC JUDGMENTS are 
arrived at by the process of deductive reasoning, as 
when it is demonstrated that "The sum of the three 
angles of a triangle is equal to two right angles". Pure 
mathematical conclusions are the outcome of mediate 
analytical judgments. 

IMMEDIATE SYNTHETIC JUDGMENTS are 
those of which the agreement or disagreement of 
the subject and predicate is warranted, not by a com- 
parative analysis of their subjects and predicates, but 
by an observed fact of experience. For example: 
"Some shrubs are thorny". There is nothing in the 
universal notion of "shrub" and "thorny" to compel 
the mind to affirm this judgment. The affirmative 
connection between "shrub" and "thorny" rests for its 
justification upon an observed sense- fact of experience. 

MEDIATE SYNTHETIC UNIVERSAL JUDG- 



INDUCTION 77 

MENTS. It is observed, for example, that a five- 
dollar gold piece and a feather placed in the ex- 
hausted receiver of an air-pump, fall through equal 
vertical spaces in equal time. Other materials are 
experimented with in the same way. The same result 
follows. Then it is concluded that "All bodies fall 
through equal vertical spaces in equal times". This is 
mediate synthetic universal judgment. 

At first sight it looks as if this conclusion is not 
justified. How is it possible to reach such a conclusion 
about all bodies, though we have experimented only 
on some? How is the mind justified in bridging the 
chasm between "some" and "all"? This leap moreover 
seems to violate the rule of reasoning that "the con- 
clusion cannot have a greater extension than the 
premises". We can clearly see the validity of the 
conclusion about the "some" on which we have actually 
experimented, but how are we justified in predicating 
of "all" what we know by experience of "some" only? 

Other examples : Science tells us that "All diamonds 
are combustible", though on very few has the experi- 
ment been performed. "All potassium floats in water" ; 
"H and O combine to form water". In fact, scientists 
admit that we may from one observed case arrive at a 
universal law. How this can be is the problem of 
scientific Induction. 

SCIENTIFIC INDUCTION— In general it is a 
process by which from comparatively few observed 
cases, we discover laws that govern the activities or 
phenomena of the material world. 

Scientific Induction comprises the following steps: 

A. OBSERVATION— Certain facts of phenomena 
presented to the senses are observed. These facts may 
become known either by observation of events in the 
course of Natural Occurrences, or by observation of 



78 ESSENTIALS OF FORMAL LOGIC 

what happens as the result of artificially arranged 
experiments. Take an example from the events of 
common life. Several persons at the same banquet 
were temporarily poisoned. This is an observed fact. 
It serves as a starting point for the investigation of its 
cause by the Inductive process. Observation of facts 
is the first step in an Inductive reasoning. 

B. HYPOTHESIS— The question is, then, naturally 
asked: How did the fact of poisoning happen? 
What was its cause? The human mind naturally 
seeks the cause of observed phenomena. The investi- 
gator examines the menu, and finds that among the 
dishes served at the banquet was lobster. He sus- 
pects the lobster may have been tainted. So among 
the antecedents of the poisoning he hits upon tainted 
lobster as the cause of that phenomenon. So far the 
cause selected is only a supposition, a tentative explana- 
tion, a clever guess. It may or it may not be the true 
cause. Such a supposed cause is called a hypothesis. 

A hypothesis, then, is a supposed cause of a 
phenomenon provisionally selected with a view of 
eventually ascertaining the true cause of the phenom- 
enon in question. Since a hypothesis is only a sup- 
posed cause, it would be irrational to accept it as the 
real and certain cause of the phenomenon which it 
professes to explain. 

Hypothesis is so called because the form of reason- 
ing in the case expressed by a hypothetical or 
conditional syllogism thus : "If the guests ate tainted 
lobster, then poisoning would follow. But poisoning 
did follow". From this syllogism we cannot conclude 
"Therefore the guests ate tainted lobster", because 
some other unsuspected cause may have produced the 
poisoning. At best the only conclusion we may validly 
draw is — "tainted lobster may possibly be the cause". 



INDUCTION V9 

Beware, therefore, of accepting a mere hypothesis, as 
popular scientific books and magazine articles too often 
do, as a final and certain scientific conclusion. 
A hypothesis to be admissible must be 

a. Possible. 

b. It must explain all the main facts of experi- 

ence in the case. 

c. It must not either in itself or in its conse- 

quences contradict any other certainty, 
known fact or law. 

C. VERIFICATION— Verification, the third step 
in an Induction, is that process by which the investi- 
gator tests whether the supposed cause (hypothesis) 
is the real, true cause of the phenomenon under 
consideration. In the example chosen, verification 
endeavors to confirm whether the real cause of the 
phenomenon — poisoning — was tainted lobster. The 
author of the hypothesis will continue his investigations 
to discover whether some other unknown agency might 
not have played a part in causing the poisoning, 
(a) He will endeavor to eliminate every possible in- 
truder, (b) He will draw conclusions by deduction 
from his hypothesis and observe whether these con- 
clusions agree in other cases, with the facts of nature, 
(c) He will continue his investigations until he is con- 
vinced that the supposed cause is the only necessitating 
cause of the phenomenon. When he is satisfied that 
the tainted lobster alone produced the poisoning, then 
he concludes that the former was the true cause of the 
latter. VERIFICATION IS THE KERNEL of the 
whole process of Induction. 

D. GENERALIZATION— The process of gen- 
eralization is based upon the rational assumption that 
constant phenomena must have their sufficient reason in 
the fixed nature of an active cause, in this case, of 



80 ESSENTIALS OF FORMAL LOGIC 

tainted lobster, which will always act in the same way. 
This constant way of action inherent in the nature of 
causal agencies is called THE LAW OF THE UNI- 
FORMITY OF NATURE. And this uniform ten- 
dency of natural agencies to act in the same way is 
not of itself a self-evident principle, like the law of 
causation, but finds its ultimate explanation in the will 
of an all- wise and omnipotent Ruler of the universe. 

Induction, then, rests on a few important principles 
which it must assume to justify its conclusions, (1) the 
principle namely of causality (analytic — self-evident) 
and (2) the principle of the uniformity of nature, 
which may be thus stated: Physical non-free causes, 
when they act in similar circumstances, always and 
everywhere produce similar results. 

Induction is usually divided into COMPLETE and 
INCOMPLETE Induction: 

COMPLETE Induction is the process by which 
we predicate of a whole class of things what we have 
already predicated from experimental reasons, of each 
individual in the class. Example : 

John, James, Henry, etc., passed successfully their 
examination in philosophy. 

John, James, Henry, etc, make up the entire class. 
Therefore the entire class passed successfully the ex- 
amination in philosophy. 

INCOMPLETE INDUCTION or Scientific Induc- 
tion is the process by which we rise to a universal 
law from our experience of a limited number of cases. 
It draws a conclusion about "all" from our experience 
of "some". It is an inference from particular to gen- 
eral, from what comes within experience to what is 
beyond experience. 

WHAT IS THE RATIONAL EXPLANATION 
OF THIS MENTAL PROCESS FROM THE PAR- 



INDUCTION 81 

TICULAR TO THE GENERAL ? It certainly needs 
justification. This justification cannot rationally rest 
upon experience itself. Experience at best extends to 
only a few cases. Hence Empirical and Positivist 
Philosophy, which teach that all knowledge is confined 
to experience, that the world outside experience is 
unknowable, utterly fail to justify their own pet form 
of reasoning, Induction. 

According to Scholastic philosophy the ultimate 
justification of the law of the uniformity of nature 
rests on the will of an all-wise Creator, Who has en- 
dowed physical agencies by His free will with regular, 
constant modes of activity. 

Incomplete Induction is so called not because it can- 
not issue in certain cases in complete certainty, but 
because all the possible cases are not, nor need they be, 
experimented upon. 

METHODS OF SCIENTIFIC INDUCTION 

THE METHOD OF AGREEMENT. When a 
phenomenon has occurred in several different cases, 
and these different cases have a single circumstance 
in common, this common circumstance is probably the 
sufficient reason or cause of the phenomenon. Briefly 
"the sole invariable antecedent of a phenomenon is 
probably its cause". Example — Suppose several per- 
sons had eaten lobster at the same meal and were 
prostrated by ptomaine poisoning, the lobster was 
probably the cause of their sickness. 

METHOD OF DIFFERENCE. "Whatever is 
present in a case when the phenomenon to be in- 
vestigated occurs, and absent in another when that 
phenomenon does not occur, other circumstances re- 
maining the same, is the cause or partial cause of that 



82 ESSENTIALS OF FORMAL LOGIC 

phenomenon". Example — A bell is rung in a jar 
containing air. The sound is heard. The air is 
removed. The bell is again struck. The sound is 
not heard. We conclude that the air is the trans- 
mitting cause of the sound. 

THE METHOD OF REMAINDERS OR RESI- 
DUES. "When the part known to result from 
certain antecedents, already determined by previous 
inductions, is eliminated from the phenomenon, that 
which is left of the phenomenon is caused by the re- 
maining antecedents". Example — My lamp has been 
lighted two hours. The temperature of my room has 
risen from 65 degrees to 70 degrees. How explain 
the additional 5 degrees ? The increase of heat is due 
to the lamp and my body. There is no fire. The lamp 
is now burned for the same length of time while the 
room is unoccupied. The temperature shows an in- 
crease of 4 degrees. I conclude that my body was 
the cause of the additional 1 degree. 

THE METHOD OF CONCOMITANT VARI- 
ATIONS. "When the degrees of variation of a 
phenomenon correspond with the degrees of variation 
of the antecedent, it is to be presumed that there is 
between the two a relation of causality, immediate or 
mediate". Example — Instead of striking a bell in a 
complete vacuum we can strike it with very little air 
in the receiver of the air-pump. We then hear a faint 
sound, which increases or decreases every time we 
increase or diminish the density of the air. This shows 
that the air is the cause of the transmission of sound. 



Chapter X 
Analogy 

48. An argument from analogy ( dxa\o7ia — propor- 
tion) is one that is based upon an equality of proportion 
between two acts or instances. There is for example a 
certain equality of proportion between the law of 
gravitation and the heavenly bodies on the one hand 
and submission to lawful authority and the citizens of 
a state on the other hand, which may be stated in 
mathematical form thus: 

Heavenly bodies : gravitation : citizens : authority. 
Hence we may argue that as 

The heavenly bodies submit to the law of gravitation 

Therefore the citizens of a State ought to submit 
to the lawful authority. 

The principle underlying an argument derived from 
an equality of proportion is : What can be predicated 
of one pair of related terms may be also predicated of 
the other pair of related terms. The conclusion is 
valid when the argument is based upon those points 
in which the relations are exactly the same, but invalid 
when based upon points in which the relations are 
different. There exists, for instance, to a certain 
extent, an equality of proportion between 

Individuals: state: members: human body. 

There are, it is true, relations between individuals 
and the State which in certain points are exactly the 
same as the relations between the members and the 
human body. Yet individuals have other relations, 
with God for example, which make the relations of 
the individual to the State different from the relations 
83 



84 ESSENTIALS OF FORMAL LOGIC 

of the members to the body. To argue, therefore, 
that just as the members are entirely subservient to 
the body so individuals are entirely subservient to the 
State, would be invalid. 

There are, in addition to this kind of argument based 
on an analogy of proportion, arguments based on an 
analogy of general resemblance. If one instance re- 
sembles another in important respects, we argue that 
what is predicable of the first instance may be pred- 
icable of the second. Thus : 

The Earth and Mars are alike in several respects— 
both are planets, both revolve round the sun, both turn 
on their axes, both have an atmosphere and change of 
seasons. 

But the earth is inhabited. 

Therefore Mars is inhabited. 

This argument is not reliable because there may be 
many important points of difference between the two 
planets. And the validity of the inference in such 
cases will depend upon the points of resemblances when 
compared with the points of difference. 

An argument from example is also based on re- 
semblances, but is more often employed to stimulate 
action rather than impart knowledge. Even when the 
purpose is knowledge, example is used rather to illus- 
trate what is already known than to discover what is 
vet unknown. 



Chapter XI 

Fallacies 

49. A FALLACY or sophism is an argument in 
which a falsehood is hidden under the appearance of 
truth. 

Divisions — 1. Fallacies arising from the "language" 
{fallacies in dictione). 2. Fallacies arising from 
the matter {fallacies in re). 

I. Fallacies in Language are : 

Equivocation — arising from the employment of 
the same word in different senses. 

Amphibology — arising from the doubtful or am- 
biguous meaning of the grammatical con- 
struction. 

Composition — when that which is true only of 
things taken separately is understood of them 
taken together. 

Division — when that which is true only of things 
taken together is understood of them taken 
separately. 

Accent — arising from the difference of stress laid 
on a particular syllable of word. 

Figure of Speech — when we mistake the meaning 
of one word with that of another whose form 
is similar. 

II. Fallacies in matter : 

Accident — where predicates that essentially be- 
long to the subject are confounded with those 
that accidentally belong to it. 

A die to secundum quid ad dictum simpliciter, and 
vice versa. 

85 



86 ESSENTIALS OF FORMAL LOGIC 

Refuting the wrong point {Ignoratio Elenchi) — 

"barking up the wrong tree". 
Begging the question — Petitio principii — Vicious 

Circle. 
Consequent — The fallacy of the Hypothetical 

Syllogism. 
False cause — non causa pro causa; post hoc, ergo 

propter hoc. 
Many questions. 
False induction — 

a. Ab uno disce omnes. 

b. False observation. 

c. Confounding a hypothesis with a scientific 

certainty. 

d. Seeing what we wish to see. 

e. Not seeing what we do not wish to see. 

f . False interpretation. 

Examples of each of these fallacies are given in the 
course of the class lectures. 



Chapter XII 

Definition 

50. DEFINITION is the expression in words of the 
nature of a thing. Definition then belongs to the Logic 
of the simple apprehension. It declares the essential 
characteristics of a thing. It has to do with Compre- 
hension. It presents a distinct idea of the subject and 
the essential characteristics stand in the predicate. It 
is this predicate that is the definition. 

KINDS OF DEFINITION. Definition is either 
real or nominal. NOMINAL DEFINITION is one 
that declares the meaning of the word. It has to do 
with the word, that is its sense or meaning in as far as 
the word is the name (nomen) of a thing. This quasi- 
definition is usually expressed by giving the derivation 
of the word defined, as "infinite" means "without limit" 
from "in" not, and "finis", a limit. 

A REAL DEFINITION is one which explains 
the nature of a thing. And it explains this nature by 
giving the characteristics of the thing. Real definition 
may be 

GENETIC (genesis — origin), which gives 
the process by which the thing is produced, 
as : A circle is a figure that is formed by 
the evolution of a line in a plane around one 
of its extremities. It does not give its 
essential characteristics, nor its properties, 
but simply tells how it has come to be. 
DESCRIPTIVE DEFINITION is one, 
which gives such a combination of prop- 
erties, accidental features, circumstances, 
87 



88 ESSENTIALS OF FORMAL LOGIC 

etc., as suffice to make the object recog- 
nizable. It is the literary definition. It 
does not enter into the essence of the 
object. 
ESSENTIAL DEFINITION is one which 
is formed by the "genus" and "specific 
difference" of a thing. This is the strictly 
philosophical definition. It gives the 
species of the thing, because the species of 
a thing is made up of the "genus" and 
"specific difference", as "man is a rational 
animal". The "essential definition" is 
rarely attained. 
Now we can give the essential definition of but few 
objects. We know a lion is different from a horse, 
but we cannot penetrate the essential difference be- 
tween them. In most cases we must be content with 
definitions by properties. 

RULES OF DEFINITION. (1) The definition 
must be clearer than the thing defined. (2) The defini- 
tion must not be negative unless in case of negative or 
privitive ideas. (3) The definition must be adequate, 
i. e., the subject and predicate must have exactly the 
same extension. (4) The definition must not contain 
the thing defined. (5) The definition must not contain 
metaphors. (6) It must be concise. Experience teaches 
that examples, which for the sake of making an im- 
pression on the memory may have a local coloring, are 
best given by the teacher in the course of the lectures. 



Chapter XIII 

Division 

51. DIVISION is the complete and orderly separa- 
tion of a unit or whole into its constituent parts. 

A unit or whole (totum) is some one thing which 
contains in itself several things into which it can be 
split up. These several things contained in a "whole" 
are called its "parts". 

There are several kinds of "units" or "wholes", 
which we must carefully distinguish. There is : 

A. The REAL unit or whole which exists in the real 
order of things. It has, therefore, real parts — "Man", 
for instance, is a real unit or whole, because "man" 
exists in the objective order of things independently of 
our mind. We can distinguish in "man" as a real 
unit or whole different kinds of parts : 

PHYSICAL PARTS, those namely that can 
be actually separated. For example "body" 
and "soul" are physical parts of "man". 
Since body and soul are essential to "man", 
they are called ESSENTIAL PHYSICAL 
PARTS. 
Other physical parts may be distinguished in 
man and likewise can be actually separated. 
But these parts, though they contribute to 
the entirety or integrity of a man, are yet 
not absolutely necessary or essential to 
man, as leg, awn, etc. A man remains a 
man though he may lose an arm or leg. 
These are called INTEGRAL PHYSICAL 
PARTS. 

89 



90 ESSENTIALS OF FORMAL LOGIC 

Again we can consider those parts in man 
which, though they cannot be really sep- 
arated one from another in "man" like the 
essential physical parts and the integral 
physical parts, yet may be mentally sep- 
arable, that is by different concepts of the 
mind. 
For instance, the "animal nature" and the "rational 
nature" in man. They can be separated, not actually 
or physically, but only in thought. Such parts are 
called metaphysical parts, and "man", considered as 
made up of such parts, is a "metaphysical whole or 
unit". 

B. There yet remains another kind of "whole" or 
"unit", and consequently other kinds of parts, namely, 
a logical or potential unit or whole and logical or 
potential parts". 

A logical or potential whole or unit is a universal 
idea". It is called "logical" because, though it repre- 
sents what actually exists (direct universal) yet its 
object does not exist in the way it is conceived in 
thought, X070S, because it is conceived by the mind 
abstracted from all individuating notes. 

It is called "potential" because it is capable of being 
predicated of many "inferiors", myriads of which do 
not exist and perhaps never will exist. For the exten- 
sion of a universal idea covers not only the individuals 
which now actually exist, or have existed, but also all 
those that may possibly be, because to all of them the 
object represented by the universal idea applies. 
RULES OF DIVISION— 

(1) A division must have one and only one basis or 
principle of division. 

(2) It must be adequate or complete. 

(3) The constituent parts must be mutually ex- 
clusive. 



91 



(4) Each step of the division must be proximate. 

(5) It must, if possible, be positive. 

The aim of definition is to make clear our ideas ; the 
aim of division is to make distinct our ideas. 



Part IV 

METHOD 

Chapter I 

Synthetic and Analytic Method 

52. Method ( tueri 6d6s ) means a way or road to- 
wards. When applied to logic it means a way or road 
which is most advantageous to follow in the attain- 
ment, exposition and defense of truth, or scientific 
knowledge. 

There are two such roads or methods, namely the 
Synthetic and the Analytic. 

THE SYNTHETIC METHOD. Some sciences 
set out from a few simple ideas and a few necessary, 
universal principles ; mathematics, for instance, is such 
a science. The mathematician then proceeds to com- 
bine these elementary notions, in order to deduce from 
them other new, less simple, more complex relations. 
He proceeds synthetically and therefore his method is 
called synthetic. 

The Synthetic Method, then, is that which proceeds 
from the universal to the less universal and particular. 
It is also called the deductive method. The sciences 
to which it is applied are called deductive sciences. 
This method predominates in philosophy and theology 
as well as in mathematics. 

THE METHOD OF ANALYSIS. When, on 
the other hand, a science starts from concrete in- 
dividual facts which observation and experiment prc- 
92 



SYNTHETIC AND ANALYTIC METHOD 93 

sent to the investigator, and aims at discovering general 
truths and laws based upon these facts, the method 
adopted is called Analytic. This is the method 
mainly employed in the experimental sciences, usually 
called the physical sciences, as chemistry, physics, 
botany, etc. 

The Analytic Method, then, is that which proceeds 
from the individual, the particular, the composite, to 
the universal or general truth or law. The sciences 
which predominantly employ this method are called 
inductive sciences. 



Chapter II 
Rules of Method 

(1) Proceed from what is simple and previously 
known to you to what is more complex and as yet 
unknown to you. 

This is what is done in the study of both Deductive 
and Inductive Sciences. What is simplest and pre- 
viously known in the deductive sciences are axioms 
and simple definitions, from which you proceed to more 
complicated and as yet unknown problems. In induc- 
tive sciences what is simplest and previously known 
are concrete individual facts of observation and experi- 
ment, from which you proceed to general laws which 
are as yet unknown. 

(2) Proceed step by step, orderly, logically, not 
hastily. Make no sudden leaps in your pursuit of 
truth, so as to leave gaps in your knowledge. 

(3) In the statement and exposition of the subject 
under investigation remove all ambiguity from the 
terms employed by exact, brief, clear definitions and 
divisions. A summary of the doctrines of your ad- 
versaries on the subject under consideration will help 
to clarify the position you are prepared to defend. 

Want of exact definitions confuses knowledge, want 
of adequate division obscures it. Besides, division 
will distinctly set before you the different parts of a 
science which demand your treatment and definition 
will marvelously clarify your knowledge. 

(4) While on the one hand we should never accept 
anything as true which we do not evidently know to 
be so, so on the other hand, we must not expect the 

94 



RULES OF METHOD 95 

same degree of certitude or the same cogency of evi- 
dence in all sciences. This rule will help to save you 
from Scepticism. 

RULES FOR STUDY 

The following rules to guide your studies may be 
suggested. They may be called the rules of Method 
in Study. 

(1) Form the habit of discovering illustrations or 

examples. 

(2) Form the habit of proceeding with order. 

(3) Form the habit of attending to the matter at 

hand. 

(4) Form the habit of perseverance in study. 

(5) Study with a pen in your hand. 



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